I just said it 10 times out loud, and it sounds like "twony". :) I have heard some people say "tweny", but I think it is most commonly pronounced "twony".

The variations on 20 are cultural, often associated with slang from music. Say it normally unless you are purposely saying it differently for whatever reason.

.... I say twOny.

I don't think I've ever heard anyone say twOny. That would be weird. First, there are two "t"s in twenty. Second, if *anything* I might hear/say "twInty" instead of "twEnty" - but definitely not an "O." No one says "twOny"