Sure, taking out the door jamb and squaring it up to match the door would be best, but that’s not all there is too it. The jamb isn’t going to come out unless the trim comes off. And it’s quite likely that you’ll damage the walls as you lever off the trim. And if you’re going to repair one small section of wall, you should really do the whole room. And if you’re repairing walls, then you’ll certainly need to repaint. But does it really make sense to repaint when you’ve got such bad windows…

The sensible solution is to carefully glue an extension of wood on the top of the door. Plane this wood to create an even, 1/8-inch-wide gap all across the door, then paint to hide the patch. Work carefully and no one will ever know.