Is there anything in canon that teaches us what the entities orbiting the planet are, their capabilities, where they come from, etc.?
I am happy to accept responses based on the expanded universe (EU).
As far as I can tell, the answer is no.
They weren't mentioned in any future TV episode, nor in any of the feature films.
I've done a quick search through all 1207 Star Trek novels and although there are fleeting mentions to the Edo and their God (referred to in the Star Trek Companion as the "EdoLord"), there don't appear to be any novels which explore this relationship in any greater detail.
They aren't mentioned in any of the classic TNG comics.
They aren't mentioned in any of the new "ongoing" Trek comics.