Dear A.,
My second son, who is now 5.5, had trouble with his head shape and the pediatrician actually referred us to a neurologist to discuss a helmet. Insurance wouldn't cover it but we would advised about other things that we could do. In the end his head returned to normal so he is fine.
Do you carry him on the right or left hip? Whichever one it is, use the opposite side. This will force him to look forward using and strengthening the muscles on the other side of his neck. Do the same thing when nursing or craddling him in your arms.
When changing his diapers and he is laying down, place your hands on each side of his head and turn it toward the side that needs to be strengthened. Hold it there for a few seconds. He may be slightly uncomfortable but will get used to it. If you do this every time you change his diapers, he'll some good exercise and stretching.
As for going to bed on his other side. Have you tried using one of those infant bed pillows? (Not sure of what proper name is.) This is a small pad with triangular styrofoam-type support pillows on each side. The baby lays between the two pillows which support him back and front so that he cannot roll over.
Hope this helps and you don't have to go the using a helmet.
M. C