To make life easy never wash all the sheets at same time. So kid’s sheets one day king sheets another day. Then you can keep sorted sheets sorted.

For the future buy different colored sheets for each bed.

For now label every tag with different sharpie. So black for king, red for twin etc. Or if you can sew sew a tiny ribbon tag or dot several places on the sheet to make it obvious what size it is.

To store put in clear spaces so king on top shelf and twins on bottom etc. or is separate bins or whatever makes sense so it once sorted you know what it is.

To make sets of sheets make them into sets so put a set in each pillowcase or fold set into and wrapped by a sheets.