The latch part is somehow vertically off by a good half inch or so from fitting in the hole. My first though is to take off the female part and fill the hole with some kind of epoxy or wood filler, and then re-drill the plate in a position where it fits. Is there a kit or some other recommendation to make this job easier?

 

Check your hinge screws first, it looks like the door has dropped down some.

 

That did not work, it seems like the frame must have settled resulting in the door being misaligned even though the hinges are screwed in all the way. Any other suggestions?

 

If it ever worked in the past, I doubt it suddenly dropped that far. Did you replace the door or latch? Is the gap around the door equal when it's closed? Is the frame flat, square, and plumb? Old house, new house? Any other settling issues like cracked plaster or sheetrock, sticky doors or misaligned cabinet doors?

Even though the hinges are tight, it's possible the door frame was not well attached to the studs and has finally just bowed and dropped enough to impede operation. Good workmanship is to install an extra long screw into the top (and sometimes middle) hinges to prevent that. They have to be long enough to hit the studs.

You could easily shim the bottom and middle hinges to bring it back. Say, 4 playing cards (or whatever) on the bottom, 2-3 in the middle?

 

Replace one of the top hinge screws with a long 3" screw that will hit the stud. It will usually lift the door a little bit. Be sure it's one of the screws closest to the door stop.

 

This house was built in the 90s, and the door was like this when we moved in. So I'm not really sure why it is so far off, but one thing I can say is the door actually does have fairly even spacing throughout the frame and the frame seems nicely shaped. In contrast, other doors in the house have problems closing due to warped/settled frames. I wonder if someone did something to fix the door closing in the past but left the latch misaligned like it is.

 

If you are convinced the door/jamb is solidly mounted to the wall, you can remove the striker plate and cut/glue a small block of wood in the upper portion of the hole so you can remount the striker plate lower. You may need to take a chisel and cut out a little of the jamb lower down.

 

Well I am not 100% sure there isn't anything wrong with the hinge/frame/jamb. This is my first time dealing with this kind of problem. Do these pictures help? It looks rectangular and evenly spaced to me.

 

Take the bottom and middle hinges loose from the jambs by removing the screws.

Tape a couple nickels to the back side of the hinge plates then put the screws back in.

Then put a 3" screw into the top hinge like I told ya.

What has evidentally happened is that the hinge side jamb has sunk lower than the latch side. Shimming the hinges is about all you can do.

Moving the strike plate like others suggested would be an easier fix.

 

What is that "over-the-door" hanger hook being used for. It is probably not the cause of the door drooping but if anything heavy is hung there it will add to the problem. The gap at the top of the door does show some misalignment.