Doors and Windows - Door doesn't fit squarely in frame

I recently bought an existing home. The back door leading to the carport is metal. The door doesn't fit squarely in the frame. When the door is closed, the gap between the door and jamb on the hinge side is larger at the top than it is at the bottom. Rain blows in under the door at the bottom edge closest to the hinge side, and sunlight can be seen coming in above the top of the door on the corner farthest away from the hinge side. I don't know whether the door was hung wrong or the jamb has pulled away from the stud on the hinge side. I suspect that the door was hung wrong because the deadbolt slides in and out easily. Can I fix this without removing the casing trim?

What you have is a parrallelogram with the top of the hinge side of the jamb being pulled away by the weight of the door. You can try getting extra long screws and screwing the hinge into the jamb and through to the stud behind it. Otherwise, you will need to remove the trim and do some shimming to get it straigt. Do this with the door closed, and shim behind the bottom hingeside corner or above the top knob side corner. Nail through the shims and into the studs and you should be sqaure.