Check out if any of the grocery stores near you sell bargin produce, then check their bargain produce every time you go to the store. Sometimes, its all too rotted. Sometimes, I get enough 10 plums perfect for making a crisp for 99 cents. Sometimes, there is a LARGE bunch of grapes with only a couple rotted grapes and the rest perfectly sweet for 99cents. Its hit and miss, and sometimes hit and miss in the same bag, but its often one of the best deals around.
Costco has some crazy deals. I bought 10 lbs of onions (well 20, 2 bags), for something like 3 dollars each bag. You just have to really stick to your list. (and of course, you need a membership, or a friend who will take you and let you "use" their membership. should not be a problem.)
Meal planning saves us so much money. So much less food goes to waste if we plan our meals, and buy what we need for those meals (plus a couple treats, example, a peach each or a bag of bargin produce etc), instead of buying what looks good and looks like about a week's worth of food. It also makes it much easier to cook during the week. Oh, today we're having pasta puttanesca. And tomarrow is lentil salad so I need to get those lentils soaking.
Find the most concentrated sources of nutrition. For instance animal fats (butter, lard, beef fat, chicken fat, fatty meat) have a lot of vitamins in minerals in a very small amount, along with a lot of other stuff needed for a pregnant lady and her babe. Whole grains offer more nutrition than refined grains, but if you can find a way to afford it, produce and fats have more nutrition for the amount of food, IIRC. (though in many places grains are cheaper. We have one store here that sells really cheap produce. many places do. do you have an asian market that sells cheap produce? that's one place to check. it can be crazy inexpensive at some of them).
Try techniques which provide more nutrition for the amount of food. For instance, cabbage is really cheap and very nutritious, but if you lacto-ferment it into sourkraut, (the only thing you need to add is salt and water and spices (opt)), there is a lot more vitamin c availible to your body, as well as enzymes which will make it easier to digest. (see the Traditional Foods forum for fermenting advice. It can be done easily in a mason jar.)
Potatoes have a good amount of nutrition in them, particularly if you eat the skins with fat. (it helps you absorb the vitamins) In fact, a lot of the cheapest vegetables are super healthy: cabbage, onions, potatoes, carrots, broccoli, brussel sprouts (cheap some places), garlic. If you prepare the same produce many ways, it will feel different. Example: Roasted broccoli one night, steamed broccoli with salt and butter another, broccoli cream sauce pasta, broccoli salad, cream of broccoli soup, broccoli in macaroni and cheese.... thats a whole week of broccoli right there, in different forms.
That's another way to get cheaper produce in many places: buy it in bulk. Most people don't think to buy produce in bulk, but you can get good deals at the farmer's market and some stores for buying by the flat or more. If it will store a while, thats a week's worth of lunches and dinners and snacks. If not, cut it, (sometimes cook it), freeze it, and use it slowly. If you bought a flat of stone fruit, and cut it up, it would cost less but you can use it for smoothies, dessert, snacks, over time (not so great just defrosted, but cook it a little with or without an added sweetner like honey, and serve with yogurt.)
See if your neighboors or anyone on freecycle has extra produce for cheap or free, or for your picking. You can also try to find a bulk buying group for larger bulk buys than you can use, (and thus steep savings).
good luck
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