*cracks knuckles*
Okay.
First things first:
The trip from California, depending on which half of the state you are coming from, can be fairly easy but it can take a while if you are coming from the northern half of the state. (That would be you are going up through Utah, across I-80, down and through Tennessee, and into North Carolina. Luckily, this time of year tends to be mild on the weather through this kind of trip.) If you're coming through the southern half of the state you'll be heading through Arizona, Texas, Georgia, and on into North Carolina. (This time of year the trip will be HOT but bearable.) I can give you pointers on EITHER route or even help you plan a route if you are uncertain which way to go. I have been both ways.
Secondly:
Cats. Or, pets in general. Pets, like children, require time and care during long trips. You'll need to give your cats access to a litter box so getting a larger crate (cats don't like sleeping or eating near their litter box) and putting on in or making regular stops and letting your kitties go might be the best bet. If you are stopping every night you can just set up a temporary space (like a paper) in the vehicle and then set up a box in the hotel room each night. Be sure to teach them that is where they go by placing them in it IMMEDIATELY.
Also, remember that cats are not very fond of riding in cars (most) and so it may be prudent to start slow and place your cats in whatever they will be riding in for gradually growing periods of time. Then start taking it and putting it in the car and going for short drives. Eventually, they will get used to it and this can make your trip much easier.
A crate is best. You don't want to let your cats have free range of your vehicle as you never know what might happen.
Thirdly:
Packing.
Eliminate anything you haven't touched in six months. Seasonal clothing and sentimental things can stay but seriously consider what you actually use and not. If you don't use it: donate it or sell it. You can make a decent amount from a yard sale and if you decide not to or can't sell it you can donate it and get a minor tax write-off. (Get a receipt!)
Clothes - don't use hangers and lay them out flat or roll them up (depending on size!) to save space. Folding actually takes more room!
Breakables - you don't need special paper for this. Just get newspaper and then when you get to your destination rub it down with a windex wipe.
Beds - depending on the vehicle you intend to move with and the size of the mattress will entirely depend on how this can be moved safely. If you're thinking of strapping it to the roof I'd not recommend that.
I'm a former army brat and a current army wife so if you have any more detailed questions in regards to moving, etc, feel free to ask! If I don't know I guarantee I know someone who does!