If we go back to Morrowind  (the third game), we can find many ancient inhabitants still roaming Solstheim in the current era. Rieklings. Werebears. Dunmer. Dragons. Skaal. Who was there first, and who has the largest claim?

Solstheim is an island located north-east of Skyrim and north-west of Vvardenfell. It is the setting for Dragonborn, and the.

Vvardenfell is in Morrowind and is the birth place of the Nerevarine (Morrowind hero). The environment of Solstheim resembles Morrowind and some of Skyrim. 

From what I've seen, the Rieklings just took over a tavern :P

Heh... Some might say Nerevarine, yes... But aren't there more ancient forces at work on the island? 

P.S: the Rieklings are all over the freaking place and according to a particular group of them at Castle Karstaag they may be direct descendants of the frost giants and trolls. But that theory might seem a bit far faetched considering the size and color of the little freaks.

True. Who do you think is the most powerful overall? The Dunmer have many powerful characters on their side, however numbers are not. Then there are the Skaal, who can survive almost any crisis.

Although, the dragons are pretty strong as well.

Back from the dead in the blink of an eye. Time to create a storm.

On a relevant note, who is the strongest powerhouse on Solstheim?

It is covered in ash (for the most part to the South) but stronger humans like the Empire and Ancient Nords have proven to be very persistent in their conquering of the island. Today the island is still as diverse and dangerous as it was in the Mythic Era.