K.K.
I agree with trying to find out if he has any food allergies. My daughter had eczema so bad that it would keep her up at night too, until I cut dairy out of *my* diet (we're nursing, and she was getting the allergens through my breastmilk). Within a week of cutting dairy, her eczema was almost completely gone.
You could try an elimination diet for him, but your son is old enough for you to start exploring allergy testing which is a lot easier than just guessing at what to eliminate. I highly recommend it - eczema is rarely just a "dry skin" issue, it's usually caused by environmental, seasonal, or food allergies and exacerbated by dry skin and irritating fragrances/lotions/detergents/soaps.
Once his eczema is gone, he'll be more comfortable and hopefully be able to sleep better! Good luck!