It's only a 24g, and you are only going across town. Don't stress. This is not nearly as back as when the poor stuff was bagged up and flown across the ocean.
Unplug everything and pack removable items in a waterproof container. Tie up cords with rubber bands or cable ties.
Get a bucket with a good lid -- a paint bucket -- new but well washed -- will do. Pull out rock and put in bucket. Cover with tank water up to about 3" from the top. Put on lid and hammer down securely. (You may want to have a paint bucket opener for when you get to the other end.)
Get a cooler. Fill with several inches of tank water. Fish go in cooler. There is not need to divide them up unless you think they will fight, and if you do put them in bags, TAPE UP THE CORNERS. Fish love to get in the corners and get squished.
Repeat. Corals can go in baggies in another cooler, or can go on the top of the rocks in the buckets. Any extra water can go in buckets. I suggest prepping a 5g bucket of fresh mixed water, well-aerated (run a powerhead in it for 24 hours.)
Leave about 1" of water in the tank with the sand. Tie up cables and wrap tank in moving blankets. Move the tank and stand together -- don't ever move a glass tank with sand and water in it because you can often get fractures. If you don't have a stand, slid the tank onto a piece of thick plywood and move carefully -- the goal here is not to torque the corners. Try very hard not to slosh the water or sand around.
Load car. Drive to destination. Reverse process. When pouring the water back in the tank, put a plate in the tank and pour the water on that, or put the rock in and pour the water so it land on the rock. You will have minimal cloudiness.
Use the 5g of new water to replace the grunge and dirty water that ends up in the bottom of the buckets.
If there is a delay while moving, be sure to get the buckets and coolers opened up and run heat and air as necessary.
Viola, tank moved. Monitor carefully for a week with your ammonia test kit
I suggest the following emergency supplies for worst case scenarios:
-several new, clean and washed Rubbermaid tubs (not Sterlite -- they often leak). Filled up to 2/3 with water, they can be emergency holding tanks in case of a catastrophic (but rare) tank failure after the move
-extra powerheads, for possible holding tanks
-extra heaters, for possible holding tanks or for temp control if needed
-air pump, airline and airstones
-Amquel+ Plus (yes, two pluses), in the unlikely event you start a new cycle