The wheel never shook (side to side vibration) and I never had a problem with spinning tires or traction in the rain, before I replaced the no flat tires and wheels with tires that anyone can change. Honda recommended a tire shop to change the wheels and I put on new tires. I noticed at high speed (65 MPH) vibration in the steering wheel and returned to the tire store. They aligned and balanced the tires. Steering wheel continued to vibrate and I still had poor traction in the rain so I took the van to Honda. They said it was a brake problem. Vibration continued even after Honda repair as did poor traction in the rain so I bought Michelin tires and had tires balance and aligned. Still vibration continues only at high speed and since it hasn't rained I don't know about the traction. I am now thinking of buying a new van. I would like to keep my Odyssey and hope you can come up with an answer.
Steering wheel shakes & no tire traction in rain on 2006 Honda Odyssey
If you put on new Michelin tires, are the wheels stock? If they are stock, then you may have an inner CV joint problem. I have seen this before, as the axle spins fast at freeway speed, it vibrates because the joint has excessive play.