I could not agree with Erin W. more.
You say you have to include meat, but what if you had just one or two vegetarian days a week? My husband thinks he needs to have meat at every meal, but when I cook vegetarian (as long is there is plenty and he can get FULL) he never even notices or cares that I didn't serve meat. Beans and rice (my favorite are black beans and brown rice) are cheap and yummy and nutritious. Dried beans especially are cheap and can be made in so many tasty ways. People think they are a pain to cook, but a little planning in advance or the use of a pressure cooker, and it's no big deal.
Buy steel cut oats and have them for breakfast. Cold boxed cereal is an absolute rip-off, has very little nutritional value, and you have to use more milk (which is getting more expensive all the time.) Steel cut oats take about 30 minutes to cook so you have to plan a little in advance, but they taste so good! My family hates regular rolled oats, but will eat steel cut, which is good because it's more nutritious anyway. I buy it in the bulk section at Whole Foods.
Make your own yogurt. It's way cheaper! It takes getting used to if you've been eating commercially produced and flavored/sweetened yogurt. You can google how to do it and buy a starter culture from Kitchen Kneads or a health food store. If you don't like the taste of it, sweeten it with Stevia extract (an herb found at healthfood stores) or put it in a smoothie.
Try breakfast for dinner one night a week. Make it a tradition! You can buy bags of wheat and grind your own flour with a quick electric mill. Use that to make a quick and easy waffle or pancake, and you've got a quick dinner with some nutrition. It's a fun sort of novelty for the kids to have breakfast for dinner, and it's super cheap.
If you do buy bags of wheat another great way to use it is to make wheat berry salad. You soak the wheat and boil it for a few minutes and they make a nice chewy base for a salad. You can google instructions and recipes. I make wheat berry salads for pot lucks all the time, and people love it!
I save on utilities by turning off my water when I'm brushing my teeth, washing dishes, etc. Use the minimal amount. Also remember to turn off lights in rooms you're not in, or don't even use the extra light if you have a lot of natural light in a room. Set your thermostat just two degrees warmer in the summer or cooler in the winter (this makes a HUGE difference in your energy bill). Unplug things that aren't in use (if the plug is easily accessible). Just turning things off doesn't save as much energy as unplugging it. Turn off the TV. Keep your freezer and fridge well stocked so you're not wasting energy on empty space. Only run your washing machine or dishwasher if you have a full load. Make sure your attic has insulation (UT gives you a tax deduction for the price of the insulation if you need to put some in) Fix the weather stripping around your windows and doors.
As far as your gas bill goes, planning your menus and grocery lists in advance so you only need to shop once a week is key! If you live close to your store and just need a couple of things, walk! I frequently put my daughter in her stroller and walk to the grocery store. I get exercise, I save gas, my daughter have a fun stroller ride; it's a win win win situation.
In fact, walk everywhere you can. If you're visiting a friend just a few blocks away, going to the park, going to the library, etc. Anything that is within walking distance, make it a habit of walking. You will get fit, lose weight, have more energy, save money, and have fun. I know it's hard with three children, but if you get a wagon or a good stroller, that's just more "resistance training" for you.
I just rattled off what came to mind, hopefully you find some of it useful.