What this comes down to is boundaries. How close you guys are will affect how diplomatic you should be.
A very close friend you suddenly stop spending time with in favor of your new girlfriend might feel abandoned, and act up a bit (a sign of immaturity, but not necessarily that he's a terrible person). In this situation you should certainly ask him to stop slandering her, but also analyze your own behavior and maybe make more of an effort to reconnect with him.
There also exists a possibility - if this is a close friend who typically has your back - that he perceives something in this girl that you don't see, in which case it's also worth it to talk things out and find out his point of view. I still think that his behavior is immature, however.
If, however, he's more of a "buddy" toward whom you feel no special loyalty, and is severely overstepping his bounds then you should not hessitate to firmly enforce your boundaries. The next time he says something take him aside and in no uncertain terms tell him that you don't appreciate his attitude, and would like him to stop. No need to be rude, but definitely make it clear that you're being serious, and be prepared to escalate things, or maybe even cut social (outside-work) contact with him if his attitude persists.
You need to decide the level of access you wish to allow these people (work mates) into your life. Consider this: if you were to quit your job tomorrow, would you maintain close contact with any of them? If the answer is no, or that you're not sure, then that's a sure-fire sign that maybe you should slowly separate them from some aspects of your life. Set up boundaries so that they understand that their opinions on your personal life are off limits. This does not mean that you need to be rude, or never hang out with them, but it does mean that some conversations, opinions, or developments in your life should remain private, and that some lines of inquiry should be deflected in the future.
For example, the only reason this person is calling your GF "Lady Evil" is because someone in that circle brought her up - why were you guys even talking about her in the first place?