Q:

How to structure Codeigniter "models" that do not come from a database table

Codeigniter models are generally tied specifically to a database table (or tables). 
We are finding that there are some objects that we use that have member variables and methods, but do not relate to a specific table in our database. 
An example of this sort of object is the OSMAddress return from the OpenStreetMap web service.  This has fields (depending on the location) of:

house number
building
street
city
country
country_code

this lends itself naturally for being passed around, so we have created a PHP class to encapsulate it. 
The trouble is, we are not sure where this class should live.   The operation to get the information is a CodeIgniter helper function, but OSMAddress is not a helper. 
We are using the standard CodeIgniter structure:

So: 

what are these classes called if they are not models? 
where should they live? 

A:

Helpers can only have a bunch of globally accessed reusable functions/methods that are used for specific purpose.  Here you can't define any class. 
I think you meant libraries, which will have classes with methods like in java.  These libraries can then be used in your controller classes as per your need.  
For eg: In your case, you are trying to get OSMAddress from a web service. 
You need to create a PHP file under library folder to define a class. 
application/library/your-file-name.php
Define a class OSMaddress
class OSMaddress{
    public function __construct() {
        //define all your variables here
    }

    //define all your web service methods here
    public function function_1(){
        //your code
    }
}

Once you are completed, load your library in your controller class
class Address extends CI_Controller{
    public function __construct() {
        parent::__construct();
        $this->load->library('OSMaddress');
    }

    public function function-name(){
         //Now call your function from the library
         $data = $this->OSMaddress->function_1();
         //function_1 will return the data
    }  
}

For more documentation, you can refer the docs
Hope this can help you.