I run into this a lot in my business (pest control) and have had similar issues in the shed since moving to Colorado. We use the heavy grade plastic storage bins and have a few mouse bait boxes in the shed. That worked well through the fall and winter. I've since placed a product called Stuff-It (
Stuffit, Copper Stuf-fit, Copper mesh, copper wool) around the full perimeter of the shed. You objective should be to keep the critters out of the shed, not necessarily just out of your bins. You can put out 100# of bait every week, but as long as the bar is open, the patrons will keep coming back!
Exclusion should be your objective. The threat of hanta virus is very real in Colorado and other areas. Read
Homepage | CDC Hantaviruses and look at the risks of exposure (inhalation and dermal) in a confined area (i.e. shed) and you'll see why I say total exclusion should be the objective, not selective exclusion.