I am sorry you find yourself in a tough situation. I know it's not easy- been there myself.
I agree with the folks who suggested feeding your dogs & cats individual meals, instead of leaving a big bowl down all the time. Especially if any of the animals are overweight (with dogs, you should be able to feel the ribs & visibly *see* the last 2 ribs). It will help you keep control over the amount of food being eaten, and will help you ration it out & plan for when you'll need to buy more.
If you can get to a Costco, Kirkland is a decent food for cheaper....but it isn't dirt-cheap. Also, like somebody else said, check farm supply stores. Tractor Supply carries a cheap store-brand food and sell it in big bags. It isn't great....but on the other hand, if you're focusing on "cheap" nothing is going to be a "good quality" food. Right now you're in a pinch though, and any food will fill their bellies & keep them from starving to death. The actual nutritional requirements of the average couch-potato dog are fairly low....your dogs will "survive" on virtually any commercial diet- you just need to focus on getting the humans in your family back on their feet!
The way I see it, is that there are plenty of dogs out there living their whole lives eating Ol' Roy and dollar-store brands. Your pets are going to be eating like this *temporarily* until the family gets back on its feet. It won't kill them. So just look for the best bargain you can find.
Other ideas- If you have friends who hunt, ask for any meat they're not going to use. This can potentially feed your family so that you have more money to spend on dog food- or if you don't like wild game, it can go to supplement the dog food. Put an ad up on Craigslist or other local sources asking for unwanted meat for your dogs & cats. This time of year is hunting season, so a lot of folks are cleaning out their freezers of last year's freezerburnt meat. It may not be great tasting for human consumption, but it can be used to supplement your dogs' diet.
Go to local butchers or meat lockers- if you're suburban you may need to look in rural areas to find an actual "butcher". (a facility that actually processes whole live animals). Ask if they can give you organ meats, scraps & other waste (anything but fat- and don't feed too much liver at once) for free or cheap. This is another low-cost way to get food to supplement your dogs' diet. Just cook everything up & mix with the kibble. (You could also feed raw, but mixing raw & kibble in the same meal is generally not advised.)
If you're not too proud to do it, you can also go around to grocery stores, talk to management & ask if they can give you meat that's too old to be sold & is going to be thrown away. It won't hurt your dogs. Corporate chains aren't likely to do it, but if you can find an independently owned store (again, look in rural areas) you might find somebody who will help you out.
As for the cat litter- I know very little about cats, but is there any reason why you can't use plain old sand? I think a 20 lb bag of sand from Home Depot runs about $4....or heck, you could use the dirt from your backyard (unless it's covered in snow ;). If nothing else you could use dirt or sand to bulk up the cat litter so it lasts longer.