It sounds like bullying. Perhaps a good strategy would be to firmly (and in a very adult type way, assuming you're both at least 18 years old) say "Hey! It's time for us to all grow up and stop this juvenile behavior!" Then I'd make a point to really try to ignore them and never say another word to them again. If they threaten you at any point or do something to your property (or leave harassing notes), it may be time to talk to the landlord, or if really bad, the police.

I wouldn't return the same juvenile behavior as revenge. Try to take the high road.