Norm Abram's Best Tricks of the Trade III
via This Old House
A: First, remove any screw that will come out the usual way. Then gently pry or pull on the hinge leaf to pull out the stripped screws a bit. Now when you push the hinge back into place, the heads of those stripped screws will stand out just enough for you to grab them with a pair of pliers, as shown. Pull each one out with a firm tug.
If the screws are still in good condition, with intact threads, remove any debris with a wire brush and reuse them.
If you plan to remount the door, you'll need to fill the stripped screw holes first. Whittle some small pieces of wood, put a dab of yellow carpenter's glue in the hole, and pack it full with the wood pieces. After the glue dries, trim off the excess bits of wood and you'll have solid material for the screw threads to bite into.