Originally Posted by
Chief
Seriously, I suspect the bearings in the hub are worn and will need replacing/adjusting. Look for a bicycle co-op/collective near you, and go learn how simple (and cheap) a hub overhaul can be.
The OP stated the wheel doesn't wobble while stationary which tells me the problem isn't loose hub bearings. I also expect is a problem with the truing and the only way to straighten these wheels is to bend them back into line.