an English semantics question

So today my roommate and I were talking about the words
ambiguity (or, something being ambiguous and obscurity (or, something being obscure) and of COURSE, a third synonymous term crept up: opaque.

she says that all three words:

1. ambiguous
2. obscure
3. opaque

are ENTIRELY different concepts.

I agree that while they can be defined in different ways, there is also room for similarity, that is: these words can ALSO serve as synonyms.

What do you guys think? How would you discriminate clearly amongst these three words?

Thanks guys! =)