Hi Tom,
First, we are talking about people here so don't say words like sloppy seconds and things like that as it is offensive, and meaningless anyway.
As we're dealing about people you should also remember her part in this. She may like the guy, but she may be doing this just to spite you. Remember it wasn't just you who had the relationship with her, it was also her that decided to have a relationship with an ex of her friend, and in fact it was her who contacted you. There seems to be a pattern here. She might not care about these things and feels it ok to be doing it, or dating ex's of friends and friends of exs might be the only thing she does care about in the relationship. In any case, you should feel lucky not to be in a relationship with her anymore as clearly she would act the same way while in a relationship - trying to get back at you for things she doesn't like, etc. That is, in this case, you lucked out not to be with her anymore even if she initiated the breakup.
Second, you can definitely ask your friend, if he is your friend, to respect your feelings. If it's just a hookup there are other women out there. If it is more than that and he has real feelings for her, he will date her anyway, as he should do, but you can still ask him not to bring her to your place.
You can also explain to him the situation and that she's probably just using him to get back at you, as she used you in her relationship with her "friend" - your ex. Say this delicately so it doesn't sound like you mean she couldn't be interested in him as otherwise he can get upset and will especially try to be annoying.
Third, if it does happen and he brings her over - deal with it! I know people where such things happened to them. It's not easy but it happens and you'll have to suck it up as you would receiving other kinds of punches to your stomach. Keep quite about it and take it.
I think you are lucky to be rid of her, but this may also teach you the kind of people you do want to be around and the kind of women you should be dating.
If your friend does bring her over, I would look for a new roommate. You can't complain though if he chooses to go out with her as people are like that and it's hard not to follow one's emotions.
Tom, you might want to read
How do I control my anger? As well as, in general:
Thinking clearly when upset