Absolutely nobody has told Strange what Joker really is. As such, when he sees the man arrive, he's just downright confused. That asshole from the library? He had a feeling the man might be magical, just because he seemed far too into all of those magic books and what not Strange had been reading, but he's certainly not aligned with the fae and can't be an angel, no angel is that obnoxious. So that leaves...very few options.

"What are you doing here?" Strange asks in return, giving Joker a downright confused frown before firing off a force bolt spell that straight up beans some poor angel in the head. They'll have to hold this conversation while fighting because Strange doesn't look like he's going to stop shooting off spells any time soon.