Soap made for humans can dry out a dogs skin. Dawn diswashing soap is semi okay , but for just washing the dog I would stick to dog shampoo. There is such a variety to choose from that you can probably find one that suits you.
You will want to help the skin and coat internally by giving omega fatty acids daily. Derm caps or fish oil are good for this however there are many supplements on the market for this, choose the one that is right for you. Using an oatmeal based shampoo for dogs is another way to help as it is more soothing to the skin.