Those are some really tough circumstances, you can do it though!
First, I suggest knowing your seasons. Right now, you will do great on tuber-type vegetables which can be the foundation of a low/no-meat diet, these are very affordable in the winter. I live just a bit north of you and we're at $1.50 for a 10lb bag in some stores! Cabbage, rutabaga, etc.
The tricky part is that the most affordable foods (beans) are high fibre.
WHITE rice, rather than whole fibre brown rice, is very very cost effective and I would suggest using it frequently if your stomach allows.
Canned fish/tuna is usually a good deal.
You don't like meat? With your budget, you can look online for affordable vegan/vegetarian recipes or head to the library for great cookbooks. Are you unemployed? If so, I would dedicate a good amount of time each day to learning how to cook/read recipes/read about foods. If you can find Mark Bittman's "How to Cook Everything" in a library, you should check it out. It will teach you how to properly butcher various cuts of meat (ie a whole chicken) which can save you a large amount (it's really shocked how much cheaper it is!!)
Here's a nice website I like: