most of my friends follow strict diets, too- so it works fine (paleo or watching macros are the most common in our group).

For you:
1. first sending you a hug!
2. why not ask to meet up at restaurant, so everyone can order what he/she prefers. Soon enough, they will realize wings, chicken ceasar salads and burgers where you ignore the bun aren't so weird. then i am sure they will ant to come back to your parties. i would buy a pack of hotdog buns if serving burgers. just send leftovers home with someone. also, same for alcohol- unless it is too tempting for you.
(just as most people expect booze at a baby shower these days)
3. making new friends is always fun. have you tried meetup .com
it is a free site to meet new friends (not dating site!) with similar interests. if you pick something like hiking or skiing or any number of interests. i would go with an activity based group, so food isn't focus.

hang in there!