2001 Honda Odyssey Several cyl solenoids burned one after a

At some point the van started shaking when the engine was running. I took it to a mechanic who said that on 2 cylinders the solenoids were burned and he replaced them. Then we took a long trip (6+ hours). On the way back the van started shaking again. I took it to the same mechanic who found and replaced another burned solenoid and also replaced spark plugs. Did not help! After a few miles of driving the shaking resumed. I suspect that there's something wrong with the electrical system. We've had a problem with this van since the moment we bought it used that during the cold season one of the automatic passenger doors would sometimes not work. We could never determine what was wrong. Do I have some sort of short circuit or some other electrical problem that puts too much load on solenoids? Or do I have something totally different? Thanks.