It's not uncommon for the screws in the post to be rusted in place. The back tire basically throws all of the moisture it picks up off of the road right at the back of the adjuster plate that those screws go in. After 40+ years they are usually stuck right where they are.
First, I would assume that your hinge pins are worn and that is allowing the door to sag. At some point somebody probably moved the strikerpost up to compensate. I will leave it up to you to search for a thread about replacing the hinge pins. It's not very hard and all of the major EB vendors sell the kits.
I had to drill out the screws on my current project to get them out. The good news is that it's possible to salvage the adjuster plate after drilling if you are careful. I started by trying an impact screwdriver bit. I made mine, which I quickly broke. You can buy a real #4 phillips impact bit and, if you are lucky, you can sometimes remove the screws. I was able to remove exactly one out of four so I got out the drill. The scews are 5/16 diameter phillips head. If you very carefully use a 1/4" drill bit you can drill the center out of the screws and then re-tap the holes in the adjuster plate. The phillips head will act like a centering hole to start the drill. Just be warned that you have to go easy to start or you will break the drill off on the jagged edge. Once you knock the corners off you should be able to drill right through the center of the screw. I couldn't find a phillips head replacement screw but I found some flat head socket cap screws at my local hardware store that were dimensionally the same. I would recommend coating the new screws with anti-sieze to slow down the rusting. Here are a few pictures that I could find. I hope they help.