I started cutting down my scraps into strips a few years ago. As time has gone one, I've decided I don't want to save all of them. Currently I am only saving 6.5" because although I can cut smaller, I can't cut bigger. I've already given away all strips under 4" and after I get the tub back from my friend, I will be giving those away too.
2.5" is very common and useful size. Even though I've given away all my 2.5" pretty much every quilt I make has that dimension, but I typically make "even" blocks, so 6", 8", 10:, and 12".
If the piece of fabric is fat quarter or larger, it goes into the fabric boxes. Smaller than that and I cut my 6.5" strip and give away the rest.
I've never found the ideal sorting situation. I keep them loosely color sorted, but maybe I only want civil war or florals or whatever. Still, with one consistent size and them all kept nicely in a box (banker sized storage box, or the size that reams of paper come in) and I can sort them quickly and easily.