I am doing more than four exercises, but those are a few that I can feel really work my abs. I think the Military press and squats are really good. Military press might hurt your shoulders.
Basically if you carry around a big bunch of weight with your free-standing body, your abs are working. Another one I've seen in a video that I might try because just looking at it I can tell it'll work is to grab a big dumbbell and hold it stiff-armed over your head and walk across the room. It was called a waiter carry, like you are a waiter holding a tray over your head.
For pullups which I can't do I use the assisted pullup machine. I also noticed a playground at the beach with a little curved bridge with a railing. I can use the bridge to get me into pullup position on the railing and try to hang on or lower myself slowly. The bridge gets in the way a little bit, but I can't figure out any other way to get my short self up to any other pullup bars. I can't do a pushup either, so I hold the planks longer and longer and move my arms further and further forward. Mountain climbers are also pretty good but I think I cheat when I do them and raise my butt too high.
Female, 5'3", 49, Starting weight: 163lbs. Current weight: 135 (more or less).
Starting squat: 45lbs. Current squat: 180 x 2. Current Deadlift: 230 x 2