I long ago moved everything inside, but basically you're going to want to limit yourself to freeze dried foods and dehydrated stuff.
Rice/Beans with the air sucked out and sealed should be good for a while, if not as long as if they were climate controlled.
Canned goods, I wouldn't trust as long as I would otherwise. Some of them will be fine, some won't. It's kinda hard to tell.
The easiest thing to do is always just up what you normally eat and rotate foods. If you do that with the canned stuff, you can store things in your unconditioned space and just not let them get that old. If normally you'd have 2 cans of black beans, and you add 10, you just rotate the cans.
Keep the unconditioned space as cool as possible. Put a fan in the shed to circulate air and keep it from becoming an oven in the summer and at least let it cool at night. You could also consider outright putting an AC in a shed and just setting it for a high temperature - keep the place at 90 or something. It'll cost power, but it's doable. If you're looking at a Garage storage - some are better than others at keeping the heat out. My current one is block (as is the house) so it does OK. But I've been in stick-built garages with no insulation that, well... they're ovens.
We live in Arizona... don't forget the water. Think about if you had a boil order and no power. Again, here is an easy place to rotate - just keep more of the nonperishable liquids in stock. But also think about grabbing a barrel or something. I like the 15gal barrels, they're man-movable if not easily. And Military Water Cans - MWC's - are good here, too, and they hold up. Aquatainers and a lot of the water storage stuff you find... they just don't.
Also; think about unused space. What's behind the couch? What's under the beds? Fill that stuff up. If that stuff is already filled... can THAT stuff go into a shed? The Artificial Xmas tree won't like the heat either, but it'll handle it better than food will.
I'm currently in a pretty big house, but I wasn't always. You need to be creative.
Rambling thoughts off.