Looks like the 2nd floor is collapsing (i.e. caving in). I'd agree with the comments on water damage, but then you say it's like that on 3 - 4 walls in every room upstairs which makes me wonder if it's more structural than just water since it's affecting interior walls as well...although water may be contributing. You'd think you might see some signs of water damage higher up, but it's all like 4' up. Since you don't own the home, I wouldn't think you'd be able to tear into the wall. I'd have it inspected by an engineer, or at the very least, have someone come out and detect for moisture behind the wall. I don't know what the device is called, but they can measure moisture levels behind the wall without having to actually go into the wall, or with only a very small opening.....but someone's going to have to go into it eventually so cutting even a 2" square shouldn't be objectionable by the homeowner. Personally, I'd be really nervous about purchasing the house unless you can get it for a really really good deal and plan on "flipping" it. Last thing I'd want to do is go to bed on the 2nd floor and wake up on the 1st floor having never left the bed.