This story provides solutions to the most common door hinge problems.
To get that satisfying "thunk" when a door closes -- rather than rattles, squeaks, or scrapes -- there must be an even gap between the door and the jamb all around; the hinges should be flush with the jamb and move freely; and the stop and the strike plate should be correctly aligned, so the door's latch easily clicks into the hole in the strike plate when the door closes.
The door itself may be solid-core, hollow-core, or made of panels. Hinges are attached to the jamb, which is attached to the house's framing on the sides and above. An interior door usually has two hinges and a heavier exterior door usually has three. Usually there is a gap between the jamb and the framing, which is filled with shims positioned near the nails.
Stop molding is positioned so the door bumps against it when closed. If the stop is too tight, the door will be difficult to close; if it is too loose, the door will rattle. On the latch side of the jamb, a strike plate is positioned over a hole in the jamb; the door's latch bolt engages a hole in the strike plate to latch the door. On an exterior door there is often a dead-bolt lock as well. The holes and strike plate must be correctly positioned for the door to close properly.
Hinges are attached to the other edge of the door with screws. They grab effectively only in solid wood (not particleboard). Long screws can be used if the door is solid wood, but shorter screws are used for a hollow-core door or a solid-core door with a particleboard core.
A squeaky hinge may only need a squirt of the right lubricant. If you see rust, first use penetrating lubricant to free rusted parts. Then apply powdered graphite or silicone lubricant for a longer-lasting solution. Also use lubricants to free a balky latch bolt.
On the jamb leaf of a hinge, long screws are effective if they can reach house framing. Where the screws would go into drywall, shorter screws are just as good.
If it still will not come out, it may be easier to remove the screws from one leaf, which will allow you to remove the door.