I'm in a PhD program and want to approach a professor that I'm interested in working with. I've already sent him a couple of emails describing my background and asking for a meeting but he hasn't responded yet (it's been a couple of weeks). I've heard that he is very busy but always looks for new students. I also couldn't find his office hours(he probably doesn't have any). Is it rude if I dropped by his office? If I do, should I ask to schedule a meeting or just start talking about my interests?
I've advised nearly 30 Ph.D. students during my academic career as a professor. My advice to you is to be careful here. You've sent him a few emails, and you've received no response. Hopefully you attached your CV to those emails. If he is looking for someone to join his research group and he thought you were an exciting candidate, he should have responded to one of your emails by now (or maybe he still will). Given that you are already in the program, he really should either invite you to meet with him or else let you know that he doesn't have an opportunity for you. Given his lack of responsiveness, maybe he isn't a very good choice as a research advisor in any event.
It is not rude to drop by his office. Office hours tend to be associated with classes so if they are not teaching this semester, they may not have office hours. Show up with a print out of your CV and one of your past publications (if you have one) and be prepared to talk, but also have your calendar available. Introduce yourself, hand over the CV and papers and tell them you would like to setup a time to meet. Go from there.