As Toider says, Sheogorath could be the Hero of Kvatch/Champion of Cyrodiil as Skyrim was released after the Shivering Isles expansion was released but we know from the expansion that Sheogorath sometimes get confused like in these memorable comments
I once dug a pit and filled it with clouds....or was it clowns.... it doesn't matter, it didn't slow him down. But it really began to smell! Must have been clowns. Clouds don't smell, they taste of butter. And tears.
Jyggalag! He is the Prince of Order. Or biscuits...no, no, Order!
so for all we know, Sheogorath saw the Oblivion Crisis and got confused that he was there, he's mad after all, however in that we do learn that Sheogorath is 2 people
- Sheogorath - The Deadric Prince of Madness
- Jyggalag - The Deadric Prince of Order
remember that after the main quest line of the Shivering Isles Jyggalag, while defeated, was freed from his curse so he wouldn't become Sheogorath again, if Jyggalag is a separate entity in Skyrim (haven't came across him yet) then we can confirm that the events of the Shivering Isles has occurred and that Skyrim's Sheogorath is the Hero of Kvatch/Champion of Cyrodiil
As for the Nerevarine from Morrowind, he/she is mentioned in Oblivion as having made an expedition to Akavir. now i remember in Morrowind somewhere that Corprus Victims couldn't age, evidence to this is Yagrum Bagarn, the last known living Dwemer. having mentioned that he was around at the time of the Dwemer's Disappearance but on another plane so he was unaffected, now
The Dwemer disappeared in 1E 700
The Fist Era ended in 1E 2920
The Second Era lasted for at least 897 years
Morrowind takes place in 3E 427
with these 4 facts, Bagarn's age is at least 3544, now since the Dwemer was researching immortality, leading to the discovery of the Heart of Lorkhanand Kagrenac's theory to tap into it to obtain the power of the divine and ascend the Dwemer to the divine to obtain immortality we can assume Bagarn's age isn't natural and is from his Corprus.
In Morrowind the Nerevarine is inflicted with Corprus and goes to Divayth Fyr for a cure, Divayth gives him one which has killed every other test subject thus far, after seeing the Nerevarine live he explains that what he created isn't actually a cure, the Nerevarine is still inflicted with Corprus however the negative effects of the despise have been removed only leaving the benefits so if Bagarn is immortal having Corprus then so is the Nerevarine (cause Divayth would see immortality as one of the benefits of the despise)
But you can die in Morrowind even after that!, well true but remember that Corprus does allow advance regeneration as Sixth House Cultists would cut off lumps of flesh from each other and eat it and it would regenerate, it's possible that in Morrowind you die before the regeneration can heal you properly.
Finally there is the Second Trail of the Nerevarine
Neither blight nor age can harm him.
this would mean that the Nerevarine can not age, since this trial comes from having the negative effects of Corprus removed this further strengthens the evidence that Corprus victims can not age. all of this would indicate that the Nerevarine is still alive in Skyrim those his/her location isn't revealed to us (the Nerevarine is mentioned in the Dragonborn DLC but i haven't played it yet to confirm)
the Last thing that could tie the Nerevarine, Hero of Kvatch/Champion of Cyrodiil and Dohvakiin together is Umbra, in Morrowind and Oblivion it can be obtained by the player and i remember in The Infernal City that the wielder at the time threw the sword through an Oblivion Portal
Sul and Vuhon both were thrown into Oblivion, and a being named Umbra took that opportunity of the barrier between worlds opening to throw a sword, also called Umbra, into Tamriel, preventing Clavicus Vile from imprisoning him in it again.
the book occurs decades after the Oblivion Crisis and the Ministry of Truth finished its fall into the city of Vivec in 4E 5 and destroyed Vivec city, which also caused the eruption of Red Mountain which made Vvardenfell even more desolated than before. Now Umbra seems to have some sort of spirit inside it as it took another form which helped it escape Clavicus Vile so if this spirit in Umbra was aware during Morrowind and Oblivion, if found in Skyrim (want to find it myself) it'll link all 3 hero's together