I usually put any piece that's half a page or more into the storage cubes with the full sheets. I did have the smaller pieces sorted and organized into plastic bags and put in a box, but right now it's gotten away from me at bit. The pieces are just tossed into the box as I go, and I "go fish" when I need something. Hoping to get back on track organization-wise!
Again if bigger pieces I put them with the themes or colors. If not I have a container dedicated to scraps and like yours it probably needs an overhaul