gzt: Love the paint the rest of the hinge suggestion. Genuine pro tip I mean it!
Stripper and a tiny paint brush and optional masking could be an option if you have the patience and no foot traffic. It will be quick if not entirely risk free.
Take one hinge off and buy a box of new hinges or at least enough to do one door at a time if they are all the same. Replace one hinge at a time. That's the part where you discover the previous installer or renovator has stripped or oversized the holes and it's just hanging on...
There's several fixes for that too. There's products out there where you can plug the oversized hole with a two part "putty" that hardens quite quickly. Araldite will do as well.
Put the putty into the hole making sure you fill the hole pretty well, once the putty has hardened place the hinge back in place, mark and drill the hole and fit a new screw. Easy. Sometimes it is easier to get the putty into the hole by drilling the hole to a much larger diameter prior to trying to fill with putty.
I just fill the stripped holes with wood glue and bang in a matchstick or two...and cut off with a chisel when set