Repair an old cylindrical hinge on an old bedroom closet
I think the first thing I would try is to remove the old hinge components and straightening them carefully.  I would clean them and file off any burs to prevent future wear.  

I think the stability of the wood around the hardware is just as important as the hardware itself and therefore, I would dedicate some time to ensuring the hinges go back properly.  I would sure up any soft, rotted, or splintered wood with glue.  I would cut some wood shims to put in the old screw holes.  I would use glue and perhaps get some new, slightly longer stainless screws.  

Patients and craftsmanship will be the key to repairing this.