The smallest scrap that I keep is 2.5 square. Over time I have discovered that very seldom use anything smaller. I have a BIG clear plastic bin that I keep all scraps in I also have a number perhaps 10 of those plastic shoe boxes that I use to store standard sized cuts that I know I use, 2.5, 3, 4, 5 long strips that are 2.5, misc. pieces of binding odds and ends and so on. I love scrappy quilts and use so more scraps than anything else. I do not sort scraps by color.
I have never given scraps to the birds but I have used snippets of yarn to the birds in the spring. I have had some very colorful nests in my area.