Morrowind:Gateway Ghost

Quick Walkthrough
#(Optional) Hear rumors about the Gateway Inn being haunted by a ghost.
#Talk to Angaredhel at the Gateway Inn in Sadrith Mora.
#Talk to Arara Uvulas about the topic.
#Talk to Uleni Heleran at the Mage's Guild in Wolverine Hall.
#Return to Angaredhel and decide which story to tell him.
#Receive a ring of choice.

Detailed Walkthrough
The Gateway Ghost
In Sadrith Mora, you'll learn that a ghost is haunting the South Turret bedchamber at the South Wing of Gateway Inn. When someone drives it out, it comes right back. It's ruining business at Gateway and Angaredhel, the Prefect, is unhappy.

Go to Gateway Inn and talk to Angaredhel. He'll give you the directions to the haunted room. He will also tell you that Mage-Mistress Arara Uvulas inspected the room but does not know why the ghost reappears or how to stop it.

Detective Work
Angaredhel advises you to speak to Arara Uvulas at the Telvanni Council House. You can kill the ghost (as many times as you want), but you cannot solve the quest in this manner.

The Council House is a big sphere located north of the docks. Speak to Arara Uvulas there about the Gateway Haunting and she will tell you that she can find no evidence of a restless spirit or ancestral influences. She suspects that a conjuration expert is involved. Ask anyone at the Council House about a conjuration expert and you'll be told that Uleni Heleran at the Mage's Guild teaches Conjuration, though she will not teach it to you.

Finding the Prankster
Go to Wolverine Hall and speak to anyone there. You'll learn that Uleni Heleran is mischievous and that she has bad feelings about Angaredhel and the Gateway Inn. Confront Uleni Heleran about the Gateway Haunting. She'll admit that it was a joke she played. She agrees to stop the haunting and gives you a note to take to Angaredhel.

Return to Angaredhel, select Work from the list of dialog options, and you will be given three choices, two of which have the same consequences:
#Explain what happened, but withhold Uleni's name
#Explain what happened, and include Uleni's name
#Explain what happened, and deliver Uleni's Papers
If you withhold Uleni's name, Angaredhel's Disposition will be lowered by 20 points.  Otherwise, if you choose either of the other two options, Angaredhel's disposition will be raised by 30 points.  Alternatively, if you killed Uleni, you will also get a 30 point Disposition boost.  Whichever option you choose, he will reward you with a choice of one of three rings: a Fighter Ring, a Mage Ring, or a Thief Ring.  You will also receive one Reputation point however you choose to complete this quest.

Notes
When you have finished the quest, you can boost the disposition of House Telvanni members in town by mentioning the Gateway haunting topic. Their disposition will increase by 20 and this method can be repeated until the disposition of the NPC is 70 or higher.
You can additionally use this method to increase dispositions with NPCs in Wolverine Hall, but there it only works if you finished the quest by not revealing Uleni Heleran's involvement.
Some people will point you towards Master Neloth when you're looking for a conjuration expert, but if you ask him about it, you get an annoyed reply ''"Conjuration expert? OF COURSE I'm an expert, idiot. I'm a mage-lord. But you think I'm sending ghosts to haunt the Gateway Inn? Get OUT of here, you fool!" and his disposition drops by 10.
If you have killed Master Neloth, his Mouth will have disappeared from the Council Hall, and you cannot complete this quest.This can be fixed by using the Console placeatpc "Arara Uvulas" 1 1 1 1
An Imperial Cult quest known as The Haunting features another Heleran causing a haunting, but this time as the ghost itself.

Bugs
 
Arara Uvulas may not have the "Gateway haunting" topic if you first killed the ghost and later talked to Angaredhel about work. Use the console to add it. The command line is: 

player->addtopic "gateway haunting"

Quest Stages