The Elder Scrolls IV: Oblivion - Game of the Year Edition

Random conjurers in the Imperial City?

It happens at the most random times. I will walk into the imperial city and someone will shout "For lord Dagon!" and they will conjure all daedric armor and look like they're with the mythic dawn. At first i didn't really care until i realized that they are actual named characters! The other day it was Ulen Anthram. It might not sound like a big deal, but I'm afraid one day it will be someone quest related. What should I do?

By the way, i don't know if this means anything, but in the main story I just went to the mythic dawn meeting place where the amulet of kings was taken and i was supposed to kill an argonian captive and get their book. I even completed the mission after with the spies near cloud-top. (I thought i would mention it, idk if it's important or not).

This is quest-related. The people who are attacking you were Mythic Dawn members among the general population. They are not quest-related, but you might miss out on funny dialogues with some of them (Else God-Hater in Skingrad, for instance) if you don't talk to them before they start going after you. This doesn't just happen in the Imperial City, but all towns in Cyrodiil.

There's nothing to worry about, this is related to the main quest and doesn't interfere with any other quests.