If the door resists being closed just as it is almost closed, then you certainly have a hinge problem. I've seen a lot of this particular problem in old houses I've lived in, where it is usually caused by excessive paint thickness on the frame and door edges at the hinge side. These faces meet before the hinges are closed, so when you force the door shut you are actually levering the hinge screws out of the wood. (Don't do that!)
You can see whether this is the problem by looking at the side of the door where the hinges are — if the door and the frame touch before the door is shut, then you have this problem. (Since you mention that there is no clearance on the hinge side, I assume this is the case.) In extreme cases, you will see the hinges lift away from the wood as you force the door shut.
You will need to fix things so that the meeting faces of the hinge plates are flush with (or above) the surface of the door and frame, rather than set below the surface (as depicted in the drawing on the right).
Planing the frame (or door) is certainly one way to do that, but I'm not a real DIYer (I just pay attention to the spaces I live in) so I don't have any experience with which to say which is the right solution. I hope I have helped illustrate the problem.
Unfortunately, it looks like you have a structural problem in the front wall or foundation of the mudroom. This is evidenced by the severe cracking in the brick to the right of the door, as well as cracking in the concrete under your threshold and at left. The picture showing cracking to the right of your door also shows more mortar above the lowest course of bricks than in between the other courses; this suggests that this problem was patched before, but has recently gotten worse.
Considering that, it is likely that structural repairs will be needed. These could be incremental fixes, reinforcing some weak parts, or a more comprehensive fix (such as replacing the mud room's foundation or footings) could be required. Furthermore, if the failure occurred because of water/drainage problems, you will want to take corrective action there to ensure it doesn't happen again.
I would recommend you call some experienced masons and general builders to assess the situation. Because the mudroom is its own addition, the worst-case scenario is that the whole addition has to be rebuilt. More likely is that some significant foundation and masonry repairs are needed, somewhere in the $1000-3000 range. Once that's done you can do the door/carpentry fixes.
Note that this can be a complex issue to diagnose in person, let alone from pictures over the internet. You'll want to get several opinions from people who know what they're doing. A structural engineer may not be necessary, but their opinion could help you distinguish between the builders who understand what's going on and the ones who just want to sell you an overpriced patch.
Best Answer
Almost any door should be hung plumb on both axes, level, and square. Not doing so results in undesirable movement due to gravity along with other adverse functional issues.
In this case, I'd hang the door roughly centered in the opening using shims, then I'd apply casing on the outside to cover the uneven gaps. Optionally case the inside as well. I'd then construct a threshold in an appropriate shape to mate to the door edges and the floor.
The ideal gap between a door jamb and the rough framing is one that's large enough to accommodate out-of-plumb and out-of-level conditions, along with room to shim. More is not helpful, but may also not be a problem if the casing is large enough.
In response to the new information provided... You have a small, lightweight shed. Level the floor by any convenient means and the door opening should return to something approaching plumb/level/square. Then you can hang the door parallel to the opening and expect it to work well.