Cut the Jamb and Pull
You can knock a jamb sideways out of its opening, but the nails or screws holding it in place put up strong resistance to the shear force you apply.
An easier way is to cut one of the sides in half with a reciprocating saw and then pull the rest straight away from the framing. You can easily pull away any nails or screws holding the doorjambs in place simply by using the leverage of the jamb itself. Make your cut at an angle so the two cut sections don't wedge against each other, preventing you from pulling them apart. This same technique works for pulling out windows.
Cut Fiberglass Surround Into Pieces
Some bathrooms are built around a shower or tub surround. This means that even if you manage to remove all the fasteners holding it in place, the odds are you're not getting that surround out the door in one piece. You're going to have to dice it up. Make the long cuts with a circular saw, and finish the curved areas with a recip saw. Wear eye protection because fiberglass throws a bunch of chips when it's cut. And a dust mask is a must—fiberglass dust is not something you want to breathe in. Most important, thoroughly investigate the areas where you'll be making your cuts, to avoid severing any electrical wires or plumbing pipes.
Cast iron tubs are ridiculously heavy. So unless it's a priceless collector's item, you don't want to have any part of moving one. Your best bet is to bust it up in place. It can be tough to get the cracking started, so begin hitting the tub at the edge. Once it does start breaking, pound your way along the smashed edges.
Throw a tarp or thick sheet of plastic over the top to cut down on flying shards of iron. And wear your safety gear, especially hearing protection—busting up a cast iron tub is like having a front row seat at a church bell convention. This tip works on just about anything brittle: old toilets, radiators, concrete laundry tubs, etc.