I would start by dumping everything on one table into a laundry basket (or two or three) so you have a bare spot to work on.
Then I would survey the places to store things in and the measurements of them. Then I would get a piece of plexiglass cut to whatever dimensions will work well. Then ruler fold whatever fits on them.
Then I would start folding and stacking so things pile neatly - just one area at a time - I would not even worry about sorting or piling by color until I had some neat stacks and a few more bare spots. Maybe at this point sort by TYPE of fabric - knits in one area, wovens in another, etc.