What ever happened to them after each game? Where was the Eternal Champion in the beginning of Oblivion? There are rumours that the Nerevarine is in Akavir, but where are the rest?

The Eternal Champion was simply said to be lost to the annals of history, but I like to think of Jauffre as the Eternal Champion (unofficially, of course) because his age is right where it needs to be for him to have been around as a young advlt in Arena, he seems to have a long (was trusted with the secret of Martin's existence since Martin's birth... that's got to signal a long relationship with Uriel), close relationship with Uriel, he seems to have quite a bit of inside knowledge about Jagar Tharn, I've no doubt he must be a skilled swordsman, being grandmaster of the Blades and all, and I can't think of a better reward for The Eternal Champion than to be made grandmaster of the Order responsible for protecting the Septim line.

As for The Agent, I believe it's been concluded that he was crushed by Numidium (perhaps stomped to death). The CoC is likely Sheogorath. I can't comment on the others other than Cyrus likely being dead due to old age (His story took place in the second era.).