A good car camping kitchen, in my mind, mimics a home kitchen.
- Propane stove(s) with a total of 2-4 burners (maybe 6 if it is a big group)
- Propane oven or grill (either propane or charcoal) depending on your menu
- Multiple lighters
- Pots, pans, and utensils suitable for the menu(s) and group size
- I like a large pot (for pasta), medium pot (vegetables), small pot (sauces), large fry pan, small fry pan, colander, and pot holders
- Depending on the menu and group size you might need larger pots and more fry pans. Make sure you check how they fit on the stove burners.
- Knives and cutting boards
- Coffee pot
- Food cooler(s) (possibly propane, solar, or electric)
- Drink cooler(s) (possibly propane, solar, or electric)
- Food storage container (durable and animal/rodent proof)
- Clean water tank(s) with an adjustable spigot minimum of 5 gallons, but at least 1 gallon of capacity per person
- I suggest bringing water from home and not trying to filter/purify stream water
- Soapy water basin(s) (2 gallon size)
- Rinse water basin(s) (2 gallon size)
- Dish towels
- Propane lantern(s): one for each working area (e.g., stove, grill, dishes, etc)
- Emergency 5-gallon water bucket
- Shelter (if rain and/or bugs are a potential problem)
All propane appliances should run off of 5 gallon central propane tank(s). This requires adapters, hoses, and T fittings. You will also want table(s) to set up on. Make sure the table fits in your car and get enough that there is space for everything.
Your plans seem a little problematic in that a group of 20 people bringing food individually or in small groups means you need a kitchen for each cooking group. That is a lot of kitchens. Ideally, you would plan a menu and have everyone contribute. Cooking for 20 is difficult, but not impossible. Two groups of 10 would be ideal in my mind.
If you really need lots of little groups, you probably want a simpler kitchen and limit what people can bring. Easiest would be for everyone to eat only dehydrated bagged meals. With only 3-5 meals (presumably only 2 dinners) you can just grill the whole time.