The majority of souls are recycled in the Dreamsleeve, losing their identity in the process.
Devout worshippers of Daedra are often bound into service in their realms.
Devout worshippers of the eight planet-Aedra may have their souls directed to the appropriate god-planet, perhaps feeding its identity.
Gods that don't fit neatly into the above two categories may have similar uses for mortal souls.
At least, this is as much as I know/believe, and can't remember where I got these knowledges. However, most of them arrive from mortal beliefs, which can sometimes be entirely wrong. "May your soul find rest in Aetherius": as far as I know, souls don't go there, at least not permanently. Sovngarde discounted, if it turns out to be in Aetherius.