I was testing the limits of Anastasia, my spinning wheel, making 2ply yarn/rope out of cotton fabric strips. It actually worked pretty well, I had a sort of yarn in the end, it is stiff and rigid but would probably make a great bag or bowl or something. Though I had lots of trouble getting it trough the wheel, it demanded lots of hand maneuvering, swearing and pleading. Maybe it would work better with thinner stripes or a more elastic fabric, Im thinking t-shirt.
I couldn't stop thinking about my grandmother, Gunnel, who had whole drawers full of balls of wind up fabric strips. She wove beautiful (trasmattor) carpets out of them.
Big needles and a simple pattern should do it.