I have a 2000 Odyssey. I would go (as I have) a hitch mounted four bike carrier on a swing arm. I have the Bauer (search, I just posted on this) which locks each bike the carrier, locks to the hitch, and swings to the right far enough to open the back fully. I also carry a Yakima Rocket Box on top (fishing poles, skis, etc.). The bikes in the back stay cleaner and saves a lot in cross wind resistance.

Best.