Soaps that have light oils for easy penetration into the skin and help cellular repair are good to use. Kukui, Apricot Kernel, and Sweet Almond oil are good for the skin and to moisturize dry skin and eczema. A person could make some great lotions with those oils. Pyrithione zinc is good for eczema, but I imagine it would not be easy to obtain without buying a bottle of Head and Shoulders. Head and Shoulders or any pyrithione zinc containing shampoo are normally used for scalp eczema. Ceramide moisturizers are supposed to be excellent for healing eczema, but some of them require a script by a family physician or dermatologist. Here is a link concerning ceramide moisturizers:
http://dermatology.about.com/od/skincar ... rizers.htmSome of these remdies may not alleviate the itching associated with eczema, but an allergist might be able to help with that. Eczema is not uncommon to people that have alot of allergies and the right anti-histamines can clear things up surprisingly well.
I hope any of this info helps.
Oh, and alot of essential oils can dry out the skin by themselves.