I just purchased a 67 impala and outer door handles barely work you really have to push hard to get door to open. Interior door handles are not opening doors at all. I haven't opened door panels yet but is this something that is adjustable inside there?
Welcome to the team. You have to take off the door panels and see what's going on with the linkage to the handles.
I highly recommend buying a manual on amazon or ebay, it's very helpful with small (or big) repairs. It details everything down to nut and bolt. assembly manual
Sounds like there is excess slop in the door latch. May be due to sagging hinges to a poor adjustment on the striker plate. As to not working at all from the inside that will probably due to the connecting rod (from handle to latch) that has fallen off (there is a spring clip that holds it in place, but any attempt to Jimmy the door to get into a locked car can knock the rod off).