A few of the go-to meals that I fed my son and his hungry horde:
I'd make pans of cut up sausages (or kielbasa, whatever was on sale) and diced apples (whatever type is cheapest). Bake them until the apples are tender, and the sausages are hot (or cooked to the appropriate temperature, depending on the package instructions). Season with a little cinnamon, and perhaps a little brown sugar. Serve in bowls.
Baked potatoes, when potatoes are cheap, can make several meals. Bake a whole bunch at once. Scoop the potato carefully out of the skins and make a hearty loaded baked potato soup. Make a huge pot because it reheats well. You can omit things like bacon and cheese in the soup and serve them on the side for toppings. Save all the potato skins and quarter them for a great potato skin feast, with sour cream, cheese, and bacon.
Save all the chicken bones from any roasted chickens. When you've got plenty, roast the bones until they're deeply colored and then make chicken stock from them (just toss several pounds of roasted bones in a huge pot of water and simmer away. Discard the bones after several hours and reduce the stock until it's really tasty.). Freeze the stock in quart size zip lock bags and use that to make inexpensive soups. You can make vegetable soups, chicken noodle soup, kale and potato and chorizo soup, there's lots of options if you have a good soup base.
Prepare a crockpot full of black or pinto beans, or get big cans of beans and heat them up. Make a huge pot of rice. Flavor the beans with lots of seasonings, chili powder, jalapenos, or whatever your preference. Make sure the beans are drained so they're not too watery. A bowl of rice and beans, if it's seasoned well and spicy, with tortilla chips or flour tortillas, can be very filling and comforting and inexpensive.
I would sometimes make huge pans of cornbread (not from a mix, just a simple cornbread recipe). And I'd stir diced ham and canned corn and and diced green chiles into the mix before baking. A little shredded cheese sprinkled on top in the last few minutes of baking made this a really substantial meal that didn't just seem like bread.
A pizza-style pasta can go a long way. Just toss cooked pasta with diced pepperoni (cut up small), diced tomatoes, some shredded mozzarella cheese and lots of spices. No need for a sauce, just pasta and pizza toppings.
You can make bread dough and knead finely diced pizza toppings into it (pepperoni, sundried tomatoes, olives, whatever). Bake as usual, and slice into nice thick slices.
A simple homemade marinara sauce can be made in huge quantities and frozen in quart size or gallon size freezer bags. It can be a pasta topping, or just served as a dipping sauce with toasted garlic bread, or it can be the basis for a taco soup (with shredded chicken or not, with lots of beans and spices and crispy tortilla strips).
A big pan of tortilla chips with pinto beans and cooked chorizo, sprinkled with shredded cheese and baked until hot can also go a long way. The chips don't have to be loaded with tons of beans and chorizo and cheese, they just need to have enough.
I think that the basics of feeding teens is having frozen bags of homemade stocksand homemade cooked black beans, bags of rice, and lots of good spices on hand. Kids seem to want lots of flavor, and something that smells good due to plenty of oregano or cumin or chiles just seems to be very appealing. Something that's flavored well doesn't need to be super-loaded with tons of meat or other ingredients. Buy Costco size bulk containers of chili powder, Montreal steak seasoning, cumin, and pizza seasonings.
I agree with the soda ban: just don't serve it. Have pitchers of water available.
You might consider going to a restaurant supply store and getting a couple of big pans, half sheet pans, and large boxes of foil and parchment paper, and a couple of large water containers. This will make your life easier.