The most widely held belief is that all the Dwemer on Nirn were removed from this Plane. It's unknown whether they were sent to a different, unknown Plane or just simply ceased to exist. The theory that they were somehow incorporated into the body of the Numidium is a minority opinion, but I don't know of any facts that categorically refute it.

However, they definitely did not become the Orsimer. Orsimer are a separate and distinct race from a different part of Tamriel and already existed well prior to the disappearance of the Dwemer.

Hello! Dwarf historian here.

The truth is neither. Dwarves could not be turned into Orcs. Their constitutions is different from Elves and the attempt would kill them. Unlike the other Races, what little has been translated contains Dwarven culture. Luckily with the study of Khuzdul and Neo-Khuzdul, one can read Dwarfish texts easily. According to oral tradition there is a massive mine elsewhere called Araudûm. There is little to suggest they could be incorporated into the Brass God - all that is known in the race vanished after the end of the Fourth Age.

Oral tradition that talks about Araudûm suggests it to be a place of great riches and joy [Gnol Korn ûl Araudûm, written sometime during the First Age].