Yup, Inspector D is right - you have pretty extensive water damage. After you have fixed the leak, then it's time to treat these walls.
As I look at your pictures, I think you may have old plaster. In the one picture near the floor, some paper has peeled away. It looks like you have painted wallpaper that has been pulled off. Or, you have the drywall face paper coming off. If your wall is plaster, that is going to be easier to correct (maybe) than if you have drywall.
Scape down and remove all bubbling, peeling material. If the stuff underneath looks solid, then I would go ahead and apply a good quality stainblocker. It might take an oil one to lock in all the heavy staining. After that, you can deal with cracks and voids. Of course, remove all loose painted wallpaper that may be there.
In one picture, the knockdown texture layer is coming loose. Use a taping knife and peel off all loose stuff as far as it goes. You will have to put on new texture to match what you removed. This kind of texture is sprayed on. If you are not confident you can do this, get a drywall contractor on the job and he should be able to do it. But, he will have to work to feather the texture into the existing edges.
In places where the plaster? is bulging, you may have to remove it and replace with thin drywall - or it may just be the final veneer coat which is loose (all this depends on whether your plaster is backed with wood lath or plaster lath). The thin veneer coat can be easily replaced with two or three layers of joint compound.
As bad as it looks, I have seen worse (but that doesn't help you much, does it?). In any case, I wish you the best.