Some children scare me...
And some parents scare me even more...
Since they seem to have no theory of personal property/ propriety, may I suggest that you start by doing a bit of renovation? You could probably get a door & lock for your sanctum at Home Depot or some such... (if you could find a "Tomb Depot" you could get one complete with ancient curse!)
Then, if you must have them in your house, that room stays locked and off limits-- and if the "little darlings" complain, well, explain to them, and their parents, why they are not allowed to use your stuff...
They do sound like kids who will be very well acquainted with the inner workings of the law-enforcement community at some point in their lives... or what's worse, feel like the way to deal with the people they don't like in their lives is to shoot up a high school...
And yes, trying to get your lives back in order after a disaster like Katrina is a tough job, but that doesn't mean they can ruin your life as well. You seem to be doing a lot for them-- surely they can do something for you in return, and apply some discipline to their progeny. They don't have to eat their young, just control them...
Just my $.02...