I see that your post clearly states that the hinge is twisted. I can't imagine the force it would have taken to bend that hinge. Perhaps it is bent. Or perhaps it is just no longer seated properly, and it needs to be removed an attached again.
If it is actually twisted, a 3" hinge from Ace Hardware should do the trick. Just make sure to patch the old holes with toothpicks and glue, and to properly pre-drill for the screws to seat the new hinge. The hinge is not mortised in and it only bends 90 degrees to close. Get a hinge with a fixed pin. Good luck.