How to repair a giant hole in plaster over drywall (maybe ?)
That looks suspiciously like somebody decided to cut a door through the wall and either gave up or decided it was too much work.  The wall construction looks like veneer plaster, which would fit with the age of the house.

Whatever method you decide to use, you're going to have to get some more framing in there. You at very least would need to replace the stud in the middle that was cut off and either cut back far enough that you can hit a stud on either side of the hole (the option I'd go with), or put in enough blocking that you have solid edges. I'd just use sheet rock for the patch and shim it out so it is flush with the rest of the wall surface.