I think this probably depends on the climate wherever you live. In humid areas you will have problems with bugs - less so in dry climates.
I find scraps can accumulate quite quickly. So I try to sort and deal with them just as quickly, too. If the scraps are strips I will store them together or cut them up in squares and keep them by the sewing machine to use them when I start and end sewing on another project. You can actually get quite a bit sewn with this system. So little by little I build up on a second project (usually just a simple 4-patch charity quilt).
Odd shaped scraps I use to make fabric collage. Just use some kind of stabilizer, spray baste it lightly, lay the scraps on top and stitch down with free motion or embroidery stitches. This will leave you with a piece of "fabric" that you can use for a small project. If you are concerned with the starch, you could wash this piece at this point also.
And then I always keep an old pillowcase by the sewing machine for the oddest or ugliest scraps. Once the pillowcase is full I sew the opening closed and have a pillow/cushion for my cat or dogs. Since it is stitched close, I can just throw the whole thing in the washing machine. This would also get rid of the starch.