I don't have an Odyssey but we just put new tires on my car. I would say to talk with someone and find out your options. The tires that are recommended for my car are performance tires and cost about $250 each. I got about 16,000 miles out of them. I really wanted Yokohama's ($125/tire) but they were sold out and back-ordered, no telling when they would be in. It was like this on every place/site we looked. I ended up with another set of Michelin's, but they are a firmer tire. The performance tires were soft, one of the reasons that we didn't get a lot of mileage out of them. We did not have the option to wait on the back-ordered tires, we were expecting a lot of snow and actually got them on in the middle of it.
I would talk to someone and see what your options are. They performance tires are standard on my vehicle, the ones we put on are not OEM but they are recognized as a replacement option.