Can I use the area above my garage for storage?
The joists are almost certainly taking some tension load (keeping the walls from spreading) from the roof, at least, unless it's very strangely built.

As is, given a quick look at load calculators and those inputs, probably not. even reducing live and dead loads to 20PSF (minimum live load for a "storage attic" and a pretty low storage load) and allowing lots of deflection, it's too much for a 2x8.

Your best/most cost-effective approach would probably be to convert rafters and joists into a truss system by adding web elements between the rafters and joists. You'll need a structural engineer, but it's the least added material. My trusses spanning 24 feet are all 2x4 material, so it should not take much to make a 2x8 lower chord carry a reasonable load without support from below. So you'll spend some money on engineering and save a good deal in getting it done, while having some peace of mind.