S.M.
Why don't you provide the plates, cups, utensils, and the basic traditional picnic food: fried chicken, watermelon, soda, birthday cake. Bring several coolers with ice, and serving utensils. Then tell your guests that you are bringing the basics, and ask each of them to bring a complementary dish, such as salads and side dishes, chips and dip, crudites, beer, and ice cream. That way you have the basics covered, but you don't have to spend too much money, and no one has to do too much.