While I think a reasonable answer is "Stand up for yourself and tell the guy he isn't your boss and to stop acting like he is," I suspect any answers suggesting that you suddenly become a bold and assertive person are not practical.
Another good way to deal with him is to always, always, always answer his questions with a question. Never give him a straight up answer. Just like the game of questions on Who's Line is it Anyway.
him: "Why are you doing it that way?" you: "Don't you do it that way ?" him: "No." you: "Why not ?" etc.
him: "When will you be done with that?" you: "What are you working on ?
him: "Why do you always answer my questions with a question ?" you: "Why do you ask so many questions ?"
It is great trick that always ends up with him going away.
Another option would be to send your boss an email, copy your annoying peer and ask "Mr. X (your boss); could you please clarify something for me: Do I report to you or Y (annoying peer) ? Thanks. Sincerely yours, You." If the response comes back to your satisfaction, print it out and post it on the wall near your desk. If not, leave.
You might also call your boss and tell him you are considering leaving. When your boss asks why, just tell him you don't like the people you are working with or you aren't happy with having two bosses, or that the roles and responsibilities are not clear here. Let him ask questions that lead to you explaining the situation. A good boss will get to the bottom of it and deal with it and you can stay. A lame boss will not and you should leave.
One more thing, you can never win this game and have the other peer NOT blame you for being the bad guy. You have to decide to let him claim you are the bad guy. That is OK as long as he stops bugging you.