Lots of good advice from Tazman! Just to add a couple of things...
I want to emphasize the parts from Tazman about keeping the fish in the dark, and not feeding. Both VERY helpful things! I would even say not to feed them for 2 days beforehand, because you have some fish that produce a lot of ammonia, real "poop machines".
5 or 10 gallon buckets with lids would be ideal for you, I think you can find them at big chain hardware stores. The lids are also helpful for keeping the inhabitants in the dark, which will help lower stress, as Tazman mentioned.
You can get an adapter for you car's lighter to run an air pump to multiple air stones or, better, sponge filters. If you use the buckets, you could drill a small hole in the top for the air line. But honestly, for 10 miles in the car, I wouldn't worry about it. You could, however, run stones or sponges in the buckets while the tank is being disassembled at the old house, and during re-assembly at the new house.
I don't know that it would be practical to have a heater in each bucket, so it may be best to make sure the car and new house are pre-heated before the fish go in, and stay at the appropriate temp.
When you get them to the new place and get the tank set up and heated to the proper temp, I would drip-acclimate them to equalize the temps. This time of year, despite your best efforts, their water temp is probably going to drop somewhat during transit. A drip-acclimation will account for this. (I know that it dropped for me this past weekend when I brought some new fish home from my local club's swap meet. My fish were bagged in a styro cooler, but they were still seriously chilly by the time I got them home. Yikes!)
Plastic storage bins, like Rubbermaid brand, or more of those 5-10 gallon lidded buckets would be good for moving the wet substrate. Just be aware of how much you fill each container, the wet substrate will probably be the heaviest thing to move.
Another helpful thing would be to do 50% water changes each day for a few days before the move, and a 50% water change right before packing everybody up. You have some fish that are known for producing a lot of ammonia (Oscar
, pleco, etc.), so clean water might be difficult to maintain without heavy water changes.
Be sure that the aquarium in completely empty before you move it. It looks like you have a 55g, and those are really easy to spring a leak on if they're moved with anything in them.
You can make sure to leave a level unpacked, put it with your fish stuff. That way you'll have it handy to level off the tank in the new place without having to dig through all your packed up boxes of tools.
I know there have been a number of threads here on moving fish, so you could use the search feature on this site.