H., forgive me if I'm repeating advice you've already received (you have a lot of repsonses, and didn't have time to sort through all of them).
My daughter had eczema as a toddler (which I was especially concerned about as my brother had a BRUTAL case as a child...bleeding, awful). My daughter's case wasn't nearly that bad, but it occasionally got pretty icky (cracked, bleeding fingers in the winter, which caused infections a couple of times, etc., but also bad patches on the backs of her knees, insides of her elbows, even sometimes on her face)
Here's what has worked for her:
First of all, we did the Aveeno oatmeal baths, and still do them from time to time, though her skin has been clear with only very occasional patches for years now. You can use real oatmeal, which is much cheaper, but if you buy the Aveeno bath in the green packet (not the blue), it isn't pure oatmeal...this one has some oils or something, and is much less sticky and gross. Also the oils seem much more suited to bathing and to removing actual dirt. I also recommend the Aveeno lotions and products in general for this condition (and I've tried EVERYTHING). Aveeno also makes a nice "anti-itch" lotion -- I'm sure that's not the actual name of it, but pretty close, sorry, but that's the shorthand in our house. Good for those moments when the poor kid is just painfully itchy!
We've done the topical creams and ointments as well, prescription and otherwise -- they are fine in the short run, but you will ultimately want to find the root of the problem if possible, obviously, as no one is comfortable rubbing cortizone all over a child on regular basis.
So, secondly, I took her to an allergy specialist. Now, there seems to be no consensus in the medical community on what "causes" eczema, but this doctor was a big believer in controlling environmental irritants. In her case, we discovered several foods to which she had a mild allergy that I never would have guessed. We found that by avoiding corn, and especially SOY her eczema all but disappeared overnight.
Now, she isn't allergic to either of these foods anymore, but it was difficult to cut out corn and soy. I swear I simply DESPISE the sugar lobby (blocking imports and forcing companies to use substitutes, mainly corn syrup -- making corn a total nightmare to avoid). It's in everything! But I digress...
I do have the name of the top allergy guy in DC if you'd like it...he's a bit of a trip, but very, very good. I liked that he leans towards minimizing medications, and attempting to address the cause of the problem.
We only rarely do the baths anymore (a precaution I still insist on sometimes, usually in the winter). Her skin is beautiful now, and we seem to be able to keep it that way with nothing more than Aveeno lotion.
Please contact me if you'd like info on this doctor, and best luck!
p.s. be very careful about soaps! I think even Dove soap is too harsh for some types of dry skin. With the Aveeno bath, and at his age, you probably don't even need soap, but there are several that will work without drying. Also, coat him with lotion when he gets out of the bath -- before you dry him -- to seal in the moisture, then just pat dry with a towel, and reapply lotion after he's dry.