Not repairable, bad job of sheetrocking...

Are you sure the house doesnt have plaster rather than sheetrock. Plaster could possibly be in very bad shape, and someone put liner paper on, to hold the walls all together, so it could be painted. Sometimes liner paper is done horizontally, but, yours was done vertically. If you are brave enough, you can try to remove it from one wall, and see just what is under it. Or another possibility, someone was lazy and didnt want to remove existing wallpaper, and just primed and painted over the top of it. That is what you get, when you paint over wallpaper too.

To me, that first photo looks like someone painted over wallpaper and part of the wallpaper is lifting. Second photo looks like a poorly taped seam and some nails popping up (or a really bad job done originally). 3rd photo -- if you mean the blue stuff, that looks like more than 2". 4th pic -- wow -- that looks like wallpaper that's been painted over, but it also looks like there are horizontal ridges too, so I'm not sure what's happening.

Hard to tell from the photos. I've run into old houses that had a kind of heavy wallpaper (I can't remember the name of it now) over the brown coat plaster instead of a finish coat of plaster. I think the paper covering was a cheaper method. But 1955 seems too recent for something like that. As for the third photo, I don't have a clue what's going on there.

All great feedback. Thank you! We had a contractor take a look at it and he's recommending skim coating all the walls. There will be a significant amount of prepping the walls prior to the skim coating. It's this or adding 1/4" rock to everything, or demoing all the walls and starting over. Neither of those options sounded appealing. If we go this route, I'll post photos of the results. Thanks again.

What did the contractor think it was? I can see that there will be a lot of prep, before skim coating. Please post a picture, once he has it all skim coated.

Looks like painted over wallpaper to me. I would take a razor knife, cut through the surface and then peel back whatever it is which is coming loose. A little very hot water with a drop or two of dish soap and a few minutes of waiting time will give you an answer on whether it is wallpaper. If it is wallpaper or wall lining paper, removing it is just tedious labor, no special skills needed.

If you want to leave it, you will still need to cut the surface and remove whatever is not well adhered to the wall, prime with oil and skim coat over. Drywalling over the surface requires removing all the trim and adding jamb extensions to the windows and doors and reinstalling trim. Not much more money if you were planning to replace trim but an additional expense otherwise. Unless there is significant damage or changes to the existing walls, I wouldn't even consider removing the wall surface; too much labor and money, too little benefit