The things I've read lately say not to cut plants back any more than you have to when you move them. The roots need food from the leaves in order to recover. If you haven't dug up the azaleas yet, can you wait to do it after they go dormant for the winter? Cutting them back now may encourage new growth that won't harden off before winter hits. It will also cut off buds for next spring's blooms.

As for the oleander, they don't survive in our area farther north, but I'd think that moving them to the south side of the house, preferably near a wall or the house that will soak up heat during the day to radiate to the plants at night would help. Good luck with all your transplanting. I'm going to be doing a lot of that once things go dormant.

catbird is right. The only source of energy for making new roots is in the leaves. They are the food factories of plants. Also, by cutting the plants back, you'll probably see a large flush of new top growth. That, too, will absolutely divert energy from root development.

Pruning the tops to compensate for root loss is a myth that needs to be left behind.

In your climate, this would be a little late in the year to prune, regardless of the reason.