I was intending to make an internet blog on the subject. Don't go stealing my idea!
Anyway, here are some of the cheapest things I have found for nutritional food that will keep you full and give you the most nutrient bang for your buck (ie, not just empty calories). This also takes into account what things are usually on sale, and the relative nutrient density of the foods compared to price.
Ok, so rice, beans, and pasta are very good foods. Almost always cheap, not too hard to cook. Fresh pasta/rice or recipe mixes that come in the box are best. $1~$1.50 per box of ricearoni or cheaper brand. As for beans, by FARRRRRRR the least expensive method is to buy them RAW/DRY. Don't buy canned, buy the dry beans and cook them. It's far cheaper that way, as you can often get beans at less than $1 per pound, which is enough to make over 6 cups of cooked beans (like 3 cans worth). Learn how to cook raw beans, rice, and pastas. Buying your beans and grains from stores that have bulk bins often means getting them for much cheaper as well.
Now that we have carbs covered, lets move on to meat shall we?
The cheapest forms of meat (calories/protein per pound of meat) are, hands down, chicken and pork. You would do well to explore all cuts of meat depending how much you have to spend, as one animal has many different cuts that come at varying prices. On the whole, pork and chicken are always the least expensive. The cheapest parts of the chicken are the leg, thighs, and wings of course, often under $1.50 per pound. Chicken breasts are the most expensive parts, but are also much denser in protein content. In other words, less meat will fill you up more if it's denser, so it's often better to go after chicken breasts if you can find them on sale at a comparable price to the dark meat. In the end you'll save more money and your food will last longer.
As for pork, the cheapest cuts are the pork shoulder/butt, sometimes called Boston butt. This is a large cut of meat that stretches along the back of the animal from the shoulders down. It is a tender cut that can have a lot of fat strewn through it, hence the cheap price. However, the fat can often be cut right off before and after cooking (and if you're really struggling for food, you wont mind the fat anyway

). This is comparable to what you'd call dark meat on the pig, and as such, it's the perfect cheap man's meat. It is really easy to find it for $1~$1.50 per pound. A big ass chunk of pure meat 10 pound in weight will last you for WEEKS and cost you only $10 or so. You cannot beat that! It's best to slow roast it so that it is cooked to tender perfection. (This is where I'd insert recipes on a blog, but I'm gonna be brief here).
Then there are also the other pork cuts that are still cheaper than most beef cuts, such as the pork loin (NOT to be confused with the TENDERloin). This is a light meat from the lower back area that is smaller and tougher than the butt, and has much much less fat. However, if you like that in your meat, go after the loin. The tenderloin is the very expensive cut of meat adjacent to the loin. Although it is perfectly moist and tender, as the name suggests, it is too expensive for this convo

.
And you can apply the same method to other animals and their cuts of meat. Don't just get stuck at picking up a steak, if you want beef, look around and find the CHEAPEST CUTS! It's still the same animal, just with varying textures that will save you many dollars!
Now on to fruits and vegies.
When buying vegies, I buy frozen. You can get a good pack of vegetables for like a buck out of the freezer section. Broccoli is always a great vegetable, as well as spinach. Very nutrient dense. When you want to go fresh, buy whatever you want, but try to stick with what's in season and/or on sale. You'll get the best quality for as cheap as possible. Since different vegies have so many different uses, it's really a matter of what you want and how much you want to pay for it at the time.
With fruits, I pretty much never buy them unless they are on sale. Every week your store will have a list of items that are on sale. I cannot stress enough that you will save yourself sooooo much time and money if you just look up your local stores online (they often have websites) and check their weekly specials. You'd be amazed at how efficient you can become at identifying what is out for pennies on the dollar every week. Know what you want from the store, see if it's on sale, and make plans to go there when its most convenient. All fruits have pretty similar nutrient profiles, so out of a selection of fruit that is on sale at the... $1 per pound price range, I just choose whatever fruits I like from that group for the week. If there aren't any fruits I like that are on sale, then I just skip it. Which brings me to another point...
BUY IT UP! If you notice something you eat a lot of is on sale, buy a lot of it! There are many ways to store fresh food so that it lasts longer, and boxed/canned good will outlast you anyway. There's no excuse not to overbuy on stuff that is on sale if you have the cash, and you know you're going to use it up. You will save yourself TONS of money by stocking up on food this way. If you notice fruit or vegies on sale for a ridiculously low price, figure out if there are any good ways to store/preserve those particular items, and then go for grab.
Ok, so then there are other food like nuts. Nuts are VERY good for you. They are mainly fat and protein with lots of vitamins and minerals, so they like little nutrient packs that have a nice calorie density too. That's good, because you want to buy as little food as possible with as much nutrition as possible! So nuts are your friends on a "poor man's diet". The rule of thumb for nuts, however, is NEVER buy them at full price. They can be pretty expensive (save for peanuts). However, around here they often go on sale for less than half the usual price, which is the time to really bulk up on the reserves you have at home. I always buy walnuts and almonds as my favs. They're usually $7 or more per pound, but sometimes go on sale for less than $4 per pound, which is when I buy a big bag of the things. Then, to keep them fresh, I store them in a ziplock bag in the freezer. Again, for rice, grains, beans, and nuts, bulk bin stores are your dearest friend. Big warehouse stores are also good for such items if you want to buy very large quantities at one time for much cheaper.
Then there are the other foods like bread and eggs. For bread, go with whole grain. Whole grain has more nutrients and fiber, which means it'll keep you full. Fiber filled foods are good for you, and get rid of hunger. It just means more food for later, fewer dollars spent. Eggs are always inexpensive. Spend some time learning the many things you can do with eggs ( for eating, not throwing

) .
Potatoes! CANNOT forget potatoes! These things can be UBER cheap (they have 10 pound bags of potatoes on sale for ONE DOLLAR at my local store this week), they pack a lot of carbs and nutrition to fill you up, and can be cooked any number of ways. They are awesome poor people food. The Irish didn't rely on them for nothing

. Plus they will survive in your pantry for a very long time.
Since by my methods you'll be doing a lot of cooking, you'll also want a lot of spices. The best way to go about getting these is to buy them from stores that allow you to scoop it up and pack it yourself (like bulk bin stores). Farmer's market type things. This is way way way cheaper than buying the jarred spices in most grocery stores which are far overpriced. If you can't do that, then I surmise buying your spices online would be very inexpensive as well. You want to be spending most of your money on food that actually gives you energy, not on the stuff that makes it taste good.
When you have a sweet tooth, avoid candy. Candy is expensive shit. Go after cookies, cakes, the baked good stuff. That's more of my personal preference, but it is also cheaper. You can go into the baking/cooking aisle and pick up a brownie mix for like $2~$3, that makes you an entire pan of sweet chocolaty goodness for uber cheap! And it's fresh! Rinse and repeat for cake and cookie mixes. Those are the absolute cheapest ways to get your sweet fix of baked goods, just bake them yourself from a box. For other sweet things, just look for junk that's on sale and go after it. It depends what you want, and how much you wanna spend.
Junk food is high in calories, so at least it'll satisfy your hunger, although it gives you no other nutrients in return. In the end, you only end up craving more food to fill that void in your gut from all those empty calories. Going as cheap as possible with wholesome food is the best route to saving money. learning how to cook will be your salvation. Relying on fast food will be to your detriment. You pay like... $4~$5 for ONE sandwich at most fast food joints when you could be using the same amount of money from store bought food that will last you the entire day! It makes no sense not to buy from the store and cook for yourself! I can get away with about $50 A WEEK for store bought foods that I cook myself, and eat like a king (less than that really, I just splurge on some things because i have the leftover cash)! You just have to be smart about what you buy and adjust your habits a bit.
So that's just a tidbit of the wealth of knowledge I have on the subject. Can't give it all away

.