[Daves55Sedan]

Aside from checking the hinges first, I would look at the number of shims behind the striker plate. Ultimately, you want the "star-wheel" on the door lock assembly to fit squarely with the teeth on the door striker plate. Too few shims may cause the star-wheel to hit the safety-latch plate. Too many shims will not only push the striker plate closer to the door, but may cause a misalignment between the star-wheel and teeth on the striker, which will cause the teeth to wear un-evenly.
If there are no problems on the latch end, a proper door-hinge adjustment may go well toward getting you squared away, but then you will need to re-adjust the striker plate to match the new door position.
I hate to say it, but these '55/56 doors are so heavy that you cant really tell easily if a hinge pin is worn down unless you remove the door altogether and then try to jiggle the hinge on its mounting bracket. If the hinge moves up and down at all, you should get new hinge pins and drive them in.