Studs cut to fit the sewer pipe -- is it ok?
You are right to be concerned, there's been a lot of support lost with such deep notches. The question is whether this is a load bearing wall or not. Given the fact that it's still standing I'm going to assume it's non load bearing. Building codes often state that notches can't be more than 40% of the width of a stud, which looks like it's been massively exceeded, it's more like 75% which isn't good. The studs are mostly doubled and tripled, but not all of them are. 

Kitchen walls often bear a lot of weight in the form of shelves or cabinets, even if they aren't holding up the house itself, so it makes sense to strengthen these. I'd at least double all of the studs and add stud shoes. Keep in mind that may still not be up to code in your area. 

This related answer has useful information on guidelines.