You can make stir fries with your meat of choice, veggies that they will eat, and sauced with a chicken broth thickened with corn starch, with a touch of sugar added. Serve with rice, or rice pilaf.
Stew would be great, again with a cornstarch based gravy.
Meatloaf, made with 2 parts ground beef, 1 part Itallian Sausage, an egg, maybe some chopped sweet peppers .
Various soups, such as egg drop, or hot & sour, not to mention beef barley, bean soup, pea soup, lentil soup, veggie soup, etc.
Thinly sliced roast beef with gravy, served with rice.
Pepper steak, made with sweet onion and sweet peppers, with cornstarch based gravy.
burgers and fries.
Roasted Chicken with rice or some type of potato, with fresh peas.
That should get you thinking of things that would be great to make and eat, that still satisfy the limitations you have to work with. Just take this time period as a challenge to get creative with the foods they can eat. Make a batch of flour-free peanut butter cookies. Peanunt butter, sugar, and eggs are the only ingredients.
Make up some flan, or rice pudding. There are a host of custards you can make, or even lemon curd (depending if eggs are considered as dairy by your picky group).
You can set out sausage trays (salami, pepperoni, summer sausage, etc.) along with various kinds of olives, pickles, celery sticks (think ants ona log), etc.
Or, if you're ambitious, you can make seperate items that will work with the individual food needs of your guests.
Or if all else fails, give them gift certificates to Denny's.
Seeeeeeya; Chief Longwind of the North