How about a big game of Spin the Bottle?
(kidding, of course...)
lurkette's right on both counts... mixer games are dopey, and you can definitely pull off "host(ess) with the most(ess)" role by making sure you don't spend more than a few minutes with each group. It sounds so "Gone with the Wind" to think of yourself as the social butterfly who needs to hop around from conversation to conversation, just making yourself available, but it doesn't need to be this way
Other things I've noticed about parties with mixed invitation lists:
1) Sometimes groups don't mind being "groups", and not mingling. This isn't always a bad thing. Sometimes events like this are good ways for groups to hang out, when they may not normally have this avenue.
2) You may have the opportunity to do some good introductions where you know people can hit it off together. For instance, maybe you know someone from school who you think would fit in well with on of your post-college crowds... invite a couple of people to walk around with you and meet people. If they're the social type, they may jump at the chance to get to know some new people this way.
Oh! and Happy birthday! What should we bring to the party?
edited for gender/PC-ness