It sounded like a controller programing problem at first. Then you said it comes on with the power off. When you say power off, did you mean you unplugged the controller? If the electrical component (controller) is completely eliminated then there can be no signal to electrically actuate the valves. Something is missing here in your explanation of whats happening.
What brand/model is the controller. Changing all the diaphragms was a mistake as they are not all going to go bad at the same time and they just do not open and close randomly as you described. I have seen controllers with bad mother boards actuate a program while in the "off " position but never when power was completely shut off to the controller.

your problem sounds like a problem I find at some of our jobs, so I must ask if the valves are where local kids can get to them. we've had kids activate valves many times and it can be very irritating.

Twinknsam. Did you ever figure out what the problem was? My controllers are unplugged too and one or two stations on my sprinklers come on and turn off after a few seconds. Have no kids in the area to mess with them so....perplexed. ...and it only happens when my well shorts out and I have to press the reset button on the well.