<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM 10-Q


     [X] QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
ACT OF 1934 FOR THE QUARTER ENDED MARCH 31, 1998
                                 -----------------


                          Commission File Number 1-9525
                                                ---------


                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
             ------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)


          NEVADA                                           75-2615944
-------------------------------                        -------------------
(State or Other Jurisdiction of                         (I.R.S. Employer
 Incorporation or Organization)                        Identification No.)


10670 North Central Expressway, Suite 300, Dallas, Texas,     75231
--------------------------------------------------------------------------------
(Address of Principal Executive Offices)                    (Zip Code)


                                 (214) 692-4700
                         -------------------------------
                         (Registrant's Telephone Number,
                              Including Area Code)




Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [X] No [ ]



Common Stock, $.01 par value                            1,519,888
----------------------------                 -------------------------------
         (Class)                             (Outstanding at April 30, 1998)




                                        1
<PAGE>   2

                          PART I. FINANCIAL INFORMATION


ITEM 1.  FINANCIAL STATEMENTS

The accompanying Consolidated Financial Statements have not been audited by
independent certified public accountants, but in the opinion of the management
of Income Opportunity Realty Investors, Inc. (the "Company"), all adjustments
(consisting of normal recurring accruals) necessary for a fair presentation of
the Company's consolidated financial position, consolidated results of
operations and consolidated cash flows at the dates and for the periods
indicated, have been included.

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                           CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                         March 31,       December 31,
                                                           1998              1997
                                                        ----------       ----------
                                                           (dollars in thousands)
<S>                                                     <C>              <C>       
                       Assets
Notes and interest receivable
   Performing ....................................      $    2,012       $    2,010

Real estate held for investment, net of
   accumulated depreciation ($5,716 in 1998 and
   $5,211 in 1997) ...............................          82,367           81,914

Investment in partnerships .......................           1,776            1,762
Cash and cash equivalents ........................             158            1,145
Other assets (including $124 in 1998 and $302 in
   1997 from affiliates) .........................           3,143            3,478
                                                        ----------       ----------
                                                        $   89,456       $   90,309
                                                        ==========       ==========

        Liabilities and Stockholders' Equity
Liabilities
Notes and interest payable .......................      $   61,140       $   61,323
Other liabilities (including $456 in 1998 and
   $468 in 1997 to affiliates) ...................           3,496            3,855
                                                        ----------       ----------
                                                            64,636           65,178

Commitments and contingencies

Stockholders' equity
Common Stock, $.01 par value;
   authorized, 10,000,000 shares; issued and
   outstanding, 1,519,888 shares in 1998 and
   1997 ..........................................              15               15
Paid-in capital ..................................          64,804           64,804
Accumulated distributions in excess of accumulated
   earnings ......................................         (39,999)         (39,688)
                                                        ----------       ----------
                                                            24,820           25,131
                                                        ----------       ----------
                                                        $   89,456       $   90,309
                                                        ==========       ==========
</TABLE>

The accompanying notes are an integral part of these Consolidated Financial
Statements.



                                        2
<PAGE>   3

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                      CONSOLIDATED STATEMENTS OF OPERATIONS


<TABLE>
<CAPTION>
                                                                     For the Three Months
                                                                        Ended March 31,
                                                                 -----------------------------
                                                                     1998             1997
                                                                 -----------       -----------
                                                                     (dollars in thousands,
                                                                       except per share)
<S>                                                              <C>               <C>        
INCOME
   Rents ..................................................      $     3,590       $     2,692
   Interest ...............................................               63                69
                                                                 -----------       -----------
                                                                       3,653             2,761



EXPENSES
   Property operations ....................................            1,461             1,340
   Interest ...............................................            1,406               877
   Depreciation ...........................................              504               365
   Advisory fee to affiliate ..............................              168               123
   Net income fee to affiliate ............................               --               124
   General and administrative .............................              216               265
                                                                 -----------       -----------
                                                                       3,755             3,094
                                                                 -----------       -----------


(Loss) from operations ....................................             (102)             (333)

Equity in income of partnerships ..........................               13                17
Gain on sale of real estate ...............................               --             1,849
                                                                 -----------       -----------

Net income (loss) .........................................      $       (89)      $     1,533
                                                                 ===========       ===========



Earnings Per Share

   Net income (loss)......................................$             (.06)      $      1.01
                                                                 ===========       ===========




Weighted average Common shares used in computing earnings
   per share ..............................................        1,519,888         1,519,888
                                                                 ===========       ===========
</TABLE>



The accompanying notes are an integral part of these Consolidated Financial
Statements.



                                        3
<PAGE>   4

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                 CONSOLIDATED STATEMENT OF STOCKHOLDERS' EQUITY
                    For the Three Months Ended March 31, 1998


<TABLE>
<CAPTION>
                                                                                         Accumulated
                                                                                         Distributions
                                                     Common Stock                        in Excess of
                                              -----------------------        Paid-In      Accumulated    Stockholders'
                                                Shares         Amount        Capital        Earnings        Equity
                                              ---------      ---------      ---------      ---------    ---------------
                                                                              (dollars in thousands)
<S>                                           <C>            <C>            <C>            <C>             <C>      
Balance, January 1, 1998 ...............      1,519,888      $      15      $  64,804      $ (39,688)      $  25,131



Dividends ($.15 per share) .............             --             --             --           (222)           (222)


Net (loss) .............................             --             --             --            (89)            (89)
                                              ---------      ---------      ---------      ---------       ---------



Balance, March 31, 1998 ................      1,519,888      $      15      $  64,804      $ (39,999)      $  24,820
                                              =========      =========      =========      =========       =========
</TABLE>




The accompanying notes are an integral part of these Consolidated Financial
Statements.



                                        4
<PAGE>   5

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS


<TABLE>
<CAPTION>
                                                                 For the Three Months
                                                                   Ended March 31,
                                                             ---------------------------
                                                                 1998            1997
                                                             ----------       ----------
                                                                (dollars in thousands)
<S>                                                          <C>              <C>       
Cash Flows from Operating Activities
   Rents collected ....................................      $    3,706       $    2,645
   Interest collected .................................              60               66
   Interest paid ......................................          (1,322)            (825)
   Payments for property operations ...................          (1,762)          (1,185)
   Advisory and net income fee paid to affiliate ......            (178)            (127)
   General and administrative expenses paid ...........            (498)            (427)
   Other ..............................................              94               60
                                                             ----------       ----------

      Net cash provided by operating activities .......             100              207


Cash Flows from Investing Activities
   Acquisition of real estate .........................              --           (1,988)
   Proceeds from sale of real estate ..................              --            1,609
   Real estate improvements ...........................            (957)            (149)
   Funding of equity partnerships .....................              (1)              (3)
                                                             ----------       ----------

      Net cash (used in) investing activities .........            (958)            (531)


Cash Flows from Financing Activities
   Payments on notes payable ..........................            (235)            (155)
   Deferred borrowing costs ...........................              --               (3)
   Dividends to stockholders ..........................            (222)            (152)
   Payments from advisor ..............................             328               19
                                                             ----------       ----------

      Net cash (used in) financing activities .........            (129)            (291)


Net (decrease) in cash and cash equivalents ...........            (987)            (615)
Cash and cash equivalents, beginning of period ........           1,145            3,186
                                                             ----------       ----------

Cash and cash equivalents, end of period ..............      $      158       $    2,571
                                                             ==========       ==========
</TABLE>



The accompanying notes are an integral part of these Consolidated Financial
Statements.



                                        5
<PAGE>   6

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                CONSOLIDATED STATEMENTS OF CASH FLOWS - Continued


<TABLE>
<CAPTION>
                                                                For the Three Months
                                                                   Ended March 31,
                                                             ---------------------------
                                                                1998             1997
                                                             ----------       ----------
                                                                (dollars in thousands)
<S>                                                          <C>              <C>       
Reconciliation of net income (loss) to net cash
   provided by operating activities
Net income (loss) .....................................      $      (89)      $    1,533
Adjustments to reconcile net income (loss) to net
   cash provided by operating activities
   (Gain) on sale of real estate ......................              --           (1,849)
   Depreciation and amortization ......................             534              396
   Equity in (income) of partnerships .................             (13)             (17)
   (Increase) decrease in other assets ................             303              (35)
   Increase in interest payable .......................              51               18
   Increase (decrease) in other liabilities ...........            (686)             161
                                                             ----------       ----------


      Net cash provided by operating activities .......      $      100       $      207
                                                             ==========       ==========
</TABLE>


The accompanying notes are an integral part of these Consolidated Financial
Statements.


                                        6
<PAGE>   7

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


NOTE 1.        BASIS OF PRESENTATION

The accompanying Consolidated Financial Statements have been prepared in
accordance with generally accepted accounting principles for interim financial
information and with the instructions to Form 10-Q and Article 10 of Regulation
S-X. Accordingly, they do not include all of the information and notes required
by generally accepted accounting principles for complete financial statements.
Operating results for the three month period ended March 31, 1998 are not
necessarily indicative of the results that may be expected for the year ending
December 31, 1998. For further information, refer to the Consolidated Financial
Statements and notes thereto included in the Company's Annual Report on Form
10-K for the year ended December 31, 1997 (the "1997 Form 10-K").

NOTE 2.        COMMITMENTS AND CONTINGENCIES

The Company is involved in various lawsuits arising in the ordinary course of
business. The Company's management is of the opinion that the outcome of these
lawsuits will have no material impact on the Company's financial condition,
results of operations or liquidity.

                          ---------------------------

ITEM 2.        MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
               RESULTS OF OPERATIONS

Introduction

Income Opportunity Realty Investors, Inc. (the "Company") invests in equity
interests in real estate through acquisitions, leases and partnerships, and has
invested in mortgage loans on real estate, including first, wraparound, and
junior mortgage loans. The Company is the successor to a California business
trust organized on December 14, 1984 which commenced operations on April 10,
1985.

Liquidity and Capital Resources

Cash and cash equivalents at March 31, 1998 aggregated $158,000, compared with
$1.1 million at December 31, 1997. The Company's principal sources of cash have
been and will continue to be property operations, proceeds from property sales,
financings and refinancings, collection of interest on its mortgage note
receivable and, to a lesser extent, distributions from partnerships.

During the first quarter of 1998, the Company paid quarterly dividends of $.15
per share or a total of $222,000.

The Company's management reviews the carrying values of the Company's properties
and mortgage note receivable at least annually and whenever events or a change
in circumstances indicate that impairment may exist. Impairment is considered to
exist if, in the case of a property, the




                                        7
<PAGE>   8

ITEM 2.        MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
               RESULTS OF OPERATIONS (Continued)

Liquidity and Capital Resources (Continued)

future cash flow from the property (undiscounted and without interest) is less
than the carrying amount of the property. For notes receivable impairment is
considered to exist if it is probable that all amounts due under the terms of
the note will not be collected. In those instances where impairment is found to
exist, a provision for loss is recorded by a charge against earnings. The
Company's mortgage note receivable review includes an evaluation of the
collateral property securing such note. The property review generally includes
selective property inspections, a review of the property's current rents
compared to market rents, a review of the property's expenses, a review of
maintenance requirements, a review of the property's cash flow, discussions with
the manager of the property and a review of properties in the surrounding area.

Results of Operations

For the three months ended March 31, 1998, the Company had a net loss of $89,000
as compared with net income of $1.5 million in the corresponding period in 1997.
Net income for the first quarter of 1997 includes a gain on sale of real estate
of $1.8 million. Fluctuations in this and other components of the Company's
revenues and expenses between the 1997 and 1998 periods are discussed below.

Rents in the three months ended March 31, 1998 were $3.6 million as compared to
$2.7 million in the corresponding period in 1997. Of the increase, $1.9 million
is due to eight properties being acquired subsequent to March 31, 1997. This
increase was partially offset by a decrease of $1.0 million due to the sale of
three of the Company's apartment complexes in 1997. Rents for the remainder of
1998 are expected to increase as the Company continues to benefit from the
operations of the properties acquired in 1997.

Property operations expense in the three months ended March 31, 1998 was $1.5
million as compared to $1.3 million in the corresponding period in 1997. Of the
increase, $786,000 is due to the acquisition of eight properties subsequent to
March 31, 1997. This increase was partially offset by a decrease of $635,000 due
to the sale of three of the Company's apartment complexes in 1997.

Interest income of $63,000 in the three months ended March 31, 1998 was
comparable to the $69,000 in the corresponding period in 1997. Interest income
for the remainder of 1998 is expected to decrease due to the expected payoff of
the Company's one mortgage note receivable in August 1998.

Interest expense increased to $1.4 million in the three months ended
March 31, 1998 compared to the $877,000 in the corresponding period in
1997.  Of this increase, $701,000 was due to the debt incurred or
assumed on seven of the eight properties acquired subsequent to March
31, 1997, and $116,000 is due to the refinancing of a property.  These



                                        8
<PAGE>   9

ITEM 2.        MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
               RESULTS OF OPERATIONS (Continued)

Results of Operations (Continued)

increases were partially offset by a decrease of $290,000 due to the sale of two
of the Company's apartment complexes subsequent to March 31, 1997. Interest
expense for the remainder of 1998 is expected to be comparable to that of the
first quarter of 1998.

Depreciation expense increased to $504,000 for the three months ended March 31,
1998 compared to $365,000 in the corresponding period in 1997. The increase is
due to eight properties acquired subsequent to March 31, 1997 partially offset
by the sale of three of the Company's apartment complexes in 1997. Depreciation
expense is expected to continue to increase as the Company acquires additional
properties.

Advisory fee expense increased to $168,000 in the three months ended March 31,
1998 compared to $123,000 for the corresponding period in 1997. The increase is
due to an increase in the Company's gross assets, the basis for such fee.
Advisory fee expense is expected to continue to increase as the Company acquires
additional properties.

Net income fee of $124,000 was incurred for the three months ended March 31,
1997. Such fee is payable to the Company's advisor based on 7.5% of the
Company's net income. No such fee was incurred in the three months ended March
31, 1998.

General and administrative expense decreased to $216,000 in the three months
ended March 31, 1998 compared to $265,000 in the corresponding period in 1997.
The decrease is primarily due to a decrease in litigation fees related to the
Olive litigation. General and administrative expense for the remainder of 1998
is expected to be comparable to that of the first quarter of 1998.

Tax Matters

As more fully discussed in the Company's 1997 Form 10-K, the Company has elected
and, in management's opinion, qualified, to be taxed as a real estate investment
trust ("REIT"), as defined under Sections 856 through 860 of the Internal
Revenue Code of 1986, as amended, (the "Code"). To continue to qualify for
federal taxation as a REIT under the Code, the Company is required to hold at
least 75% of the value of its total assets in real estate assets, government
securities, cash and cash equivalents at the close of each quarter of each
taxable year. The Code also requires a REIT to distribute at least 95% of its
REIT taxable income plus 95% of its net income from foreclosure property, all as
defined in Section 857 of the Code, on an annual basis to shareholders.

Inflation

The effects of inflation on the Company's operations are not quantifiable.
Revenues from property operations generally fluctuate proportionately with
inflationary increases and decreases in housing



                                        9
<PAGE>   10

ITEM 2.        MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
               RESULTS OF OPERATIONS (Continued)

Inflation (Continued)

costs. Fluctuations in the rate of inflation also affect the sales value of
properties and, correspondingly, the ultimate gain to be realized by the Company
from property sales. To the effect that inflation affects interest rates, the
Company's earnings from short-term investments and the cost of the new
financings as well as the cost of its variable note financing will be affected.
Inflation also has an effect on the Company's earnings from short-term
investments.

Environmental Matters

Under various federal, state and local environmental laws, ordinances and
regulations, the Company may be potentially liable for removal or remediation
costs, as well as certain other potential costs, relating to hazardous or toxic
substances (including governmental fines and injuries to persons and property)
where property-level managers have arranged for the removal, disposal or
treatment of hazardous or toxic substances. In addition, certain environmental
laws impose liability for release of asbestos-containing materials into the air,
and third parties may seek recovery from the Company for personal injury
associated with such materials.

The Company's management is not aware of any environmental liability relating to
the above matters that would have a material adverse effect on the Company's
business, assets or results of operations.

Year 2000

The Company's advisor has advised the Company that its current computer software
has been certified by the Information Technology Association of America ("ITAA")
as year 2000 compliant. The Company's advisor has also advised the Company that
it has recently received and plans to install in 1998 the ITAA certified year
2000 compliant operating system for its computer hardware.

                         ------------------------------

                           PART II. OTHER INFORMATION

ITEM 1.        LEGAL PROCEEDINGS

Olive Litigation.  In February 1990, the Company, together with
Continental Mortgage and Equity Trust ("CMET"), National Income Realty
Trust and Transcontinental Realty Investors, Inc. ("TCI"), three real
estate entities with, at the time, the same officers, directors or
trustees and advisor as the Company, entered into a settlement of a
class and derivative action entitled Olive et al. v. National Income
Realty Trust et al. pending before the United States District Court for



                                       10
<PAGE>   11

ITEM 1.        LEGAL PROCEEDINGS (Continued)

the Northern District of California and relating to the operation and management
of each of the entities (the "Olive Litigation"). On April 23, 1990, the Court
granted final approval of the terms of a Stipulation of Settlement.

On May 4, 1994, the parties entered into a Modification of Stipulation of
Settlement dated April 27, 1994 (the "Olive Modification") that settled
subsequent claims of breaches of the settlement that were asserted by the
plaintiffs and that modified certain provisions of the April 1990 settlement.
The Olive Modification was preliminarily approved by the Court on July 1, 1994,
and final court approval was entered on December 12, 1994. The effective date of
the Olive Modification was January 11, 1995.

The Court retained jurisdiction to enforce the Olive Modification, and during
August and September 1996, the Court held evidentiary hearings to assess
compliance with the terms of the Olive Modification by various parties. The
Court issued no ruling or order with respect to the matters addressed at the
hearings.

Separately, in 1996, legal counsel for the plaintiffs notified the Company's
Board of Directors that he intended to assert that certain actions taken by the
Board of Directors breached the terms of the Olive Modification. On January 27,
1997, the parties entered into an Amendment to the Olive Modification effective
January 9, 1997 (the "Olive Amendment"), which was submitted to the Court for
approval on January 29, 1997. The Olive Amendment provides for the settlement of
all matters raised at the evidentiary hearings and by plaintiffs' counsel in his
notices to the Company's Board of Directors. On May 2, 1997, a hearing was held
for the Court to consider approval of the Olive Amendment. As a result of the
hearing, the parties entered into a revised Olive Amendment. The Court issued an
order approving the Olive Amendment on July 3, 1997.

The Olive Amendment provides for the addition of four new unaffiliated members
to the Company's Board of Directors and sets forth new requirements for the
approval of any transactions with certain affiliates until April 28, 1999. In
addition, the Company, CMET, TCI and their shareholders released the defendants
from any claims relating to the plaintiffs' allegations and matters which were
the subject of the evidentiary hearings. The plaintiffs' allegations of any
breaches of the Olive Modification shall be settled by mutual agreement of the
parties or, lacking such agreement, by an arbitration proceeding.

Under the Olive Amendment, all shares of the Company owned by Gene E. Phillips
or any of his affiliates shall be voted at all stockholder meetings of the
Company held until April 28, 1999 in favor of all new Board members added under
the Olive Amendment. The Olive Amendment also requires that, until April 28,
1999, all shares of the Company owned by Gene E. Phillips or his affiliates in
excess of forty percent (40%) of the Company's outstanding shares shall be voted
in proportion to the votes cast by all non-affiliated shareholders of the
Company.




                                       11
<PAGE>   12

ITEM 1.        LEGAL PROCEEDINGS (Continued)

In accordance with the Olive Amendment, Richard W. Douglas, Larry E. Harley and
R. Douglas Leonhard were added to the Company's Board of Directors in January
1998 and Murray Shaw was added to the Company's Board of Directors in February
1998.


ITEM 6.        EXHIBITS AND REPORTS ON FORM 8-K

(a)   Exhibits:

<TABLE>
<CAPTION>
Exhibit
Number                                Description
--------      --------------------------------------------------------------
<S>            <C>
 27.0          Financial Data Schedule, filed herewith.
</TABLE>

(b)   Reports on Form 8-K as follows:

      A Current Report on Form 8-K, dated December 30, 1997, was filed with
      respect to Item 2. "Acquisition or Disposition of Assets," and Item 7.
      "Financial Statements and Exhibits," which reports the acquisition of
      Akard Plaza and Fireside Thrift Building filed January 9, 1998.




                                       12
<PAGE>   13

                                 SIGNATURE PAGE



Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                                 INCOME OPPORTUNITY REALTY INVESTORS,
                                 INC.



Date:      May 4, 1998           By:  /s/ Randall M. Paulson
     -----------------------        ------------------------
                                    Randall M. Paulson
                                    President



Date:      May 4, 1998           By:  /s/ Thomas A. Holland
     -----------------------        -----------------------
                                    Thomas A. Holland
                                    Executive Vice President and
                                    Chief Financial Officer
                                    (Principal Financial and
                                    Accounting Officer)




                                       13
<PAGE>   14

                    INCOME OPPORTUNITY REALTY INVESTORS, INC.

                                   EXHIBITS TO
                          QUARTERLY REPORT ON FORM 10-Q

                    For the Three Months Ended March 31, 1998


<TABLE>
<CAPTION>
Exhibit                                                                    Page
Number                         Description                                Number
---------           ------------------------------------------------      ------
<S>                 <C>                                                   <C>
 27.0               Financial Data Schedule.
</TABLE>




                                       14