Google "vibration in an 05 Honda Odyssey" and be prepared to read a snoot full about owners with brand new Odys with the problem. (Edmunds forums for example), And then be prepared, if you go ahead with a purchase, to experience it yourself. I just about guarantee it. I bought mine because they're rated by Edmunds to be the best van but Hondas have had tranny and motor mount problems since the 90s and now this. Evidently Honda doesn't believe in testing their products. Also their batteries are too small to handle the electronics in these things. Get the biggest one you can find.
Lots of bells and whistles - dynamite stereo.
Fire the quality control officer or whatever he's called.
We struggled with vibration in the front for the first few years of owning this van.
Started with the original tires as they wore, got new tires, problem got much worse.
Spent several hundred dollars balancing, re-balancing, road-force balancing, etc, none of which was covered under warranty.
Eventually threw out a 6 month old set of tires because it was impossible to stop the vibration and put on a set of michelins.
Again had to spend extra money to have them road-force balanced, but the vibration was eventually minimized.
Not eliminated for sure, but at least you could drive on the highway without the vibration numbing your hands and forearms.
Just one of many many issues with this van though, the vibration issue is just a drop in a large bucket.