My daughter had eczema as an infant so I've done some extensive research on eczema products. Make sure you read the ingredients before you buy a product. And be sure that they're fragrance free.
Mustela makes a line of eczema/sensitive skin products with gentle ingredients and no fragrance, etc. called Stelatopia. They make a product called Milky Oil Bath. I used it until my daughter was 2. I also used their cream cleanser for the days I wasn't giving her an oil bath. These products can get pricey, though. I bought them when Babies R Us was having deals. For shampooing the hair, I just used Babyganics fragrance-free shampoo and body wash (but didn't use it to wash the body).
Also, Cerave recently started making baby bath products. Cerave's baby wash is what I use now to wash my daughter and my 14 month old because my daughter's eczema isn't as bad as it used to be.
For moisturizing, I've been using Aveeno's Eczema Therapy Moisturizing Cream. Use it IMMEDIATELY after the bath while the skin is still moist/damp. Using a cream immediately after the bath will help the moisture to be sealed in.
Aquaphor was recommended by my pediatrician, but did not work as well as the Aveeno eczema cream. You'll have to try a few products to find the right one for your son. Check out the National Eczema Association website for other product recommendations. Also, ask his pediatrician if he should use hydrocortisone cream.