A door hinge screw doesn’t hold if it is not hitting the 2 x 4 stud that is behind the doorjamb. The doorjamb is a 3/4-inch thick board that is shimmed about 1/2-inch away from the 2 x 4 in the wall. Your door hinge screw isn’t reaching the 2 x 4. To reach the 2 x 4 through the jamb you will need a 2-1/2-inch screw with a #10 diameter. The longer screw will go clean through the doorjamb and into the wood stud. Grabbing into the stud is usually enough to draw the hinge tight and pull your door off the jamb and the threshold. Do not waterproof the basement wall on the inside article.
A heavy solid oak door will rub at the top edge when the door closes. It also binds on the threshold on the same side. People replaced the hinge screws with thicker ones trying to draw the door upright, but whatever you do they still come loose. And plastic wall anchors is morally wrong to do to wood.
Occasionally the distance to reach the 2 x 4 will call for longer screws. I have had to use 3-1/2-inch screws to secure a door in an older home I once owned.
Leave plastic anchors for plaster and cement. They are too slippery to get a grab into wood. If the anchors had sharp teeth to prevent them from slipping you would be all set.
When a hole gets too large for a screw, I have two methods to strengthen the wood when a 2 x 4 is not available.
First I coat the stripped hole with two-ton epoxy using a toothpick. Do not plan to fill the hole with epoxy, just reduce the diameter and harden the soft wood with a thin coat of glue. Do not insert the screw until the epoxy is hardened or you will risk the effect of turning the screw into a fat nail.
If the wood is too damaged for epoxy to work, try plugging the hole with a dowel. Drill a hole in the wood significantly larger than the screw hole. Do not be afraid to go to a 3/8- or 1/2-inch hole. Coat the hole and the dowel with carpenter’s glue and tap it in flush. Let it dry then drill a pilot hole and re-install the screw. This should be in for good now.