While the existing installation obviously doesn't meet current code approval if your household is like mine, the budget just won't reach a complete redo without a bit of preplanning, therefore you will no doubt have to consider making this a maintenance job for the time being.
With that in mind, i would begin by cutting out the damaged section as square as possible.
In most instances when repairing sheetrock it is difficult to make a joint between the repair sheetrock and the existing sheetrock on the existing studs. A simple solution is to sister in a short cripple stud to make a nail surface for the new sheetrock. To do so you cut a short piece of stud a couple inches longer than the vertical section to be repaired. Slip it into the wall cavity and screw it to the existing stud. You can then screw the new sheetrock to the cripple on either end. Mud and tape the joints, then apply your finish.
