If the party is sponsored by an Orthodox organization, then you may be more properly dressed as a woman if you wear a top with a higher neckline and covering the shoulders and elbows and a skirt or dress that extends below the knees.
Otherwise, Chanukah is a "newer" Jewish holiday (i.e. not from the Torah) and its days are not "chagim" (holy days with Shabbat-like restrictions on activities). So there is less that you need to know because there aren't really any bad "mistakes" I can think of a guest making. Celebrating is just a matter of lighting candles (or oil lamps) and possibly eating oil-cooked foods (but the foods aren't required and there is no ritual that goes along with eating them, unlike say Passover or Sukkot). There will probably be singing of various songs that you won't know, but if some are in English and they have song sheets, and you have a good musical sense and pick up tunes quickly, you may be able to sing along. My own personal frustration is that my tongue is too slow to sing the Chanuka song "Mi Yimalel", which is especially beautiful when sung as a round. Here is a Youtube version that has an English version as well: www.youtube.com/watch?v=KHSrRy_Tceo