We love Cetaphil cream and Cera Ve cream, both come in tubs. You want some good, super thick moisturizer. I know other people really love Eucerin and that's a good one, too. It needs to be a cream and NOT a lotion. If that doesn't kick it, you'll probably want to go see a pediatric dermatologist (your pediatrician can refer you). Lather him up in creams twice a day - morning and night. As soon as he gets out of the bath, lather him up asap.
Also, you'll want to make sure that laundry detergent and bath soap and shampoo is all fragrance-free and dye-free. This is very important because kids with eczema are super sensitive to that stuff.
Also, if derm or ped prescribes a steroid cream, always opt for the weakest percent hydrocortisone. You can even buy 1% over the counter and try that first, and then cover it with your moisturizing cream. If that doesn't cut it, then you can go up to the stronger one. I personally don't like to use steroid creams on my little guys, so I only use it when it's really bad and use it sparingly. But sometimes, it's the only thing that works.
Many times, eczema is the body's response to something that is bothering him - sometimes food allergies or other things, so you might also want to consider going to an allergist or seeing what is in his environment that could be bothering him.
FYI - Winter is the worst time for eczema, so hopefully with summer coming, it should improve! Good luck!