The timeline in the UESP indicates that Black Marsh seceded from the Empire a year after the Oblivion Crisis ended, and Elsweyr soon after. I'm assuming that data came from the novel Infernal City, which I don't have. Are there any details? Was it just a note that said "We're gone, bye!" or military action, or what?

At present I'm assuming that Gideon and Stormhold, and the northern part of Elsweyr, would remain much as they were, and it would be the interior of Black Marsh, and the south or Elsweyr that would become more independent from, or even inaccessible to the Empire. I.e. that the borders would be uncertain again.

All needed for mod background, for events happening after the Oblivion main quest.

Black Marsh became fully independent under the rule of the An-Xileel (who had full contact with the Hist). They seceded because the Argonians themselves managed to defeat Dagon's forces on their own by flooding through the Oblivion Gates and forcing Dagon to close the gates from his side. They did this all via the Hist and the An-Xileel and all without the aid of the Empire.

The An-Xileel who were already Anti-Empire saw no reason to continue to be a province and so they secede.

Therefore all of Black Marsh (now named Argonia) would be anti-Empire and anti-foreigners. So, the remaining Empire would have near to no influence.

I haven't read the books myself but I see no reason to believe there was any kind of conflict between the Empire and Elsweyr, after the Oblivion crisis there were a lot of problems in the Empire and nothing to really unify them, provinces as such had a really easy time claiming independence.

There are lore notes at the Imperial Library from http://www.imperial-library.info/content/infernal-city-lore-notes and http://www.imperial-library.info/content/lord-souls-lore-notes.

Though I recommend reading the novels, they're good and quick reads.