If you must lift on the handle to get them to close, the the upper hinge needs to be moved away from the door latch. The bottom one may need the same thing but I would try to just do the top one first.
First I would close the door almost all the way so it stops where you need to start lifting. Look at the door where it starts to hit. It sounds like it will only be hitting at the top to confirm.
Remove the door by unscrewing the screws that go into the door jamb. Take a chisle and remove the same distance of material by which the door is hitting.
If your screw holes are worn you may need to use longer and/or wider screws to bite into the wood a bit more so the door is solid.
My constant project is my home which was built in 1947. We have remodeled almost all of it and added 1000 square foot in 2007. Lars Construction got me up to drywall and I did the rest.
It sounds like the hinge screws are loose. Snug them with a screw driver before trying anything else. I usually replace the center screw on the jamb side of the top hinge with a screw long enough to penetrate the framing. The long screw provides extra support for the door and can be used to make minor adjustments to the fit of the door.