Does each mic require its own track, or can you use a small mixer and send all outputs to mono or stereo? If seperate tracks are required, there are several soundcards with multiple inputs. Check out the Delta series cards from M-Audio. Does the computer have a multitrack recording application installed? You'll need one of those if each mic needs its own track.
Check out http://www.zzounds.com for all the stuff you're looking for, including wireless mics. Their search engine is easy to navigate with.

Thanks, jonyoung!

I think Delta 1010LT will work for me. http:// is also a good place to find the things that I need.

I need to record each mic on a separate track. Ideally, I need to be able to access each mic via DirectX or other programming interface and program my own recording (I need to sync with some other programs) but this is not critical.

I hope there is some multichannel recording software that comes with the card. If not, I assume I can use Cakewalk or other recording program. By the way, with multichannel recording programs, can I save each track as a separate sound file (MP3)?

I don't know about Cakewalk's ability to save a file as mp3, but Sonar (a Cakewalk product which I use for mixing) can. The Delta card will not include any recording software, so you'll have to budget for it. Give yourself enough time to tweak your system and get familiar with your software of choice, they all have learning curves.