We've discussed furoshiki before: the Japanese idea of using a cloth to wrap and carry things, which has made a comeback in these environmentally-conscious times. I believe I mentioned that furoshiki could be many sizes, and here's an example of just that: a furoshiki made out of a bed sheet. Instructables user keng forms it into a gigantic bag, then stuffs the bag with pillows, which he can then carry away and store.
Keng discusses squaring an existing sheet, hemming the edges, and folding and tying into a sling-style bag with a shoulder strap. The bag can be used to move or store a lot, but when you're done with it, you can just fold it up into the same flat packet as a regular bed sheet.
This page of standard American sheet measurements should give you an idea of which size you'd like to use; King size is very nearly square on its own. You might also consider trying this project with upholstery fabric, which should give you a square at least four feet long on each side.
In our previous article on this topic, I linked to the following video, about a famous furoshiki shop in Japan: How to FUROSHIKI wrapping (1:17). The video shows how to make a shoulder bag of average size with a square of cloth. This project is exactly the same thing on a larger scale, so between the tutorial and the video, you should have no problem making a bag that will allow you to easily wrangle and tote almost anything you can actually manage to lift.
(I think it would be useful for a quick clean-up of kids' scattered toys when guests are on the way!)