This guys claims to eat (at home) on $36 a month.

I can vouch for oatmeal, raisins, bananas and eggs. Cheap, nutritious, keeps well.

I've survived days at a time on GORP. Cheap but surprisingly difficult to resupply. Small groceries rarely have convenient pack sizes.

In North America, peanut butter on bread/tortillas is quite convenient.

Pasta is cheap but requires a lot of fuel (and water). Rice is more economical -- pour boiling water (1 third more water than rice) and wait for 15 minutes. Search the Internet to build a list of recipes you like. I have personally never bothered shopping for dried veggies. A can of tuna mixed with rice is good enough. Fresh fruits/veggies when possible.

Tea is cheaper than coffee.

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Lots of accounts of people stealth touring, so this is most certainly a viable option. Done this myself on occasion, but it raises the question of sanitary facilities.