The way I see it, if it's a problem regarding pets, then many CF won't mind if it is posted, as many of us are pet-fanatics.
Do you live near campus? Usually, those apartments are usually small, and somewhat expensive. Look to see if there are apartments about 20 or more miles away from campus. Usually, 2 bedroom apartments far away from campus can cost as much as an effiency apartment near campus (however, it's more costly since you do have to commute.) That should help the litter box problem, but is more costly in the long-run.
As far as the moves, cats do get used to things very easily. My soon to be duh brother and moo sister-in-law have moved a lot, and their cats haven't really have any problems as far as that is concerned. One isn't bothered at all since it's moved more times than what they have (they also adopted it from a pet shelter). The other one was okay after about two days, even though it was the first time it moved.
Usually, cats grow out of things like knocking over lamps and such. However, some don't, and my two didn't. What I did is used something similiar to what they do for obedience training for dogs. I call it reverse clicker training. Instead of using a clicker to praise a dog, I made them learn to associate the sound of the clicker to being hit with a newspaper. In other words, they did wrong, I made a sound with the clicker, and tapped them on the head with the newspaper (which they really hate.) Now, whenever they hear the clicker, they think they're going to get tapped with it. But, when they stop doing the thing they were doing wrong, I rewarded them with treats they love so much.
It took them a while to learn, but at least now they know when they hear the clicker, they know they're doing something wrong, and stop immediately (it's a very rare occasion that I even have to use the clicker anymore, and they haven't even been tapped with the newspaper for such a long time). If they don't learn by what I did (try finding something they really hate, even if it's a loud screetch, but don't make it torturous--the more painful it is, the less it will work), try looking up behavior modification techniques, or any kind of behavioral type of training. if you can't find any, try finding a senior psychology major in a highly behavioristic/Skinnerian/Pavlovian psychology department.
If you can't reach an agreement with your parents, see if they'll take care of your cats while you're in grad. school. Having them take care of your cats is definitely better than taking them back to the pet shelter.
Good luck on your graduate studies and the pet situation.