Definately avoid the strawberries. My wee sister has got bad eczema. She avoids all E-numbers, tomatoes, strawberries and maybe carrots as well, I don't know. She also has to avoid stress. The body has got a lot of natural hydrocortisone if you don't want to use hydroortisone cream. The skin sets the natural hydrocortisone free if you wash the eczema with cold water. Then put vaseline (or better 50/50) on. If it flares up badly you should get some hydrocortisone cream on. Humovate and Fucibet seem to help her, Trimovate help as well if there is a fungal infection, too.
One thing... if there is EVER anybody you know with impetigo please please please keep him away from that person until it is healed. We had a horrible experience with impetigo and eczema, it was all over her body, everywhere

Good luck!
BTW, eczema also goes hand in hand with asthma and hayfever so there are a few precautions to take...
Don't overdo it with the dairy, remove all flowers from the house, don't give him any nuts or peanut butter...