This is a very involved topic, so forgive me if I don't cover everything right off the bat.
Morrowind is especially complicated because you have a lot of different institutions with degrees of power, and the Empire has an added, redundant layer of governance under King Athyn Llethan of House Hlaalu. So, at the top, you theoretically have the Emperor - except Morrowind is largely autonomous under the terms of the Armistice. Llethan, up until his death/murder circa 3E 426-7, was a complete figurehead. His replacement, Hlaalu Helseth, much less so.
For much of 3E 418-4E 0, the authority over Morrowind rested with the Tribunal - i.e, the Tribunal Temple, i.e., House Indoril. Then beneath them are the Great Houses. The Indoril are like the cops in a city full of gangs. From one perspective, they're just another gang - but they're the gang every other gang has to contend with, and you don't wanna be in their sights. It had been that way since post-Battle of Red Mountain, as far as I know. But House Hlaalu was gaining on Indoril during this time due to their close relationship with the Empire (which was fostered by Uriel VII since before the events of Arena). After the events of Morrowind, Helseth clearly filled the power vacuum, and flexed his new muscle and political acumen by outlawing slavery.
In the year or so following the Oblivion Crisis, however, Helseth and House Hlaalu will be seeing at least the beginning of a fierce backlash. The Empire, and thus House Hlaalu, were being seen as traitors due to the Imperial Legion's abandonment of much of Morrowind (or at least, that's how Redoran history records it).
Then, outside of all of this, you have the disunited Ashlanders, each with their own Ashkhans (as well as Wise Women).
So ... that's Morrowind.
Skyrim is easy- Emperor, High King in Solitude, Jarls. They're likely relatively united at this point in history- besides a witch in Whiterun and persistent necromancer troubles.
A big problem with making deductions in some of these other areas is that there's a good chance the Empire has their parallel governmental structure attached to the existing system. Many provinces (in troubled times, at the very least) have a Military Governor appointed by the Emperor. This Governor could serve to make the Emperor's vassal a complete figurehead. Or, as was the case with Morrowind, the Empire's representative could be the figurehead, with some other native political (or criminal) organization holding the real power. How the Empire classifies and considers things might be substantially different than how they are in "reality".
ESO has a lot of new lore on the Bosmer. In particular,
this one might give you a better understanding of their political structure. But that's all I got time for today.