I read that the best thing to do when moving a cat is to bring them in and leave them in one room for a while. Then let them into another room one by one every few days. If the cat goes under the bed or runs to a closet, just let it. At this time it might need a small and dark place to sit and be calm. It will come out when it feels more secure, and making it come out will only scare it more.
If you let them outside, you might have to really watch them or they might bolt away from you. But if you have some kind of outdoor area you can put them where they can't get away, you can stay with them and let them look around. Or hold the cat and walk around with it, so it can look around a little. You might have to leash a very skittish cat. I had a cat that moved to a new area and when he was out for the first time he just looked at me when I put him down on the ground. He didn't run away. He just walked around but kept me in sight. I followed him around everywhere he went, and then I took him back inside after a few minutes. I did this for a few days and he learned the lay of the yard and where the food was, so he didn't run away. Cats will walk around and maybe rub on stuff to establish their scent in the area. Some cats may scent mark, especially male cats. This isn't to anger you, but they will be in a new place so they might pee to get their scent in the area. This makes them feel more secure but is pretty smelly to you if they do this inside the house. There is this thing you can buy from vets that looks like a glade plug in. It has some cat scent in it, but you can't smell it. I think it is pheromones or something only a cat can smell. If you get one, it is supposed to make the cat feel more secure inside a new house.
Some kind of cat pheremone spay:
Click here
The plug in thing:
Click here
I don't know if those will help but it might be worth a try.
DiscordantEdit: Added some more code so the links wouldn't stretch the page.