I have a few fitted diapers that are pretty much useless too. We got them second-hand (I wouldn't be surprised if they were third- or fourth-hand) from somebody who gave us a big garbage bag of baby clothes when I was pregnant, and they just don't work very well anymore. Besides just being generally dingy and kinda gross (not even the sun would take out these weird stains in them during the sunniest summer days), they don't absorb well. They're pretty much at the garbage (or compost, I see from a post on this thread) or rag stage. But, like you said, it's kind of awkward for rags because of the shape, thickness, and elastic.
I like Heather's suggestion for the doubler, but these are past that point.
So assuming I do go with the rag idea, anyone have any 'specialty rag' ideas? Like, are these amazing at a certain cleaning task? A couple of these used to be flannel...well, still are, I guess, but not so fuzzy anymore! And the other one is regular ol' cotton.