There were three generations of the Odyssey. The first generation was peculiar in that it started out with 4 swing open doors. This made for an awkward entry into the minivan market for Honda, as by that time most American buyers were used to a single sliding door on their minivans.
There were two trim levels on these original Odysseys: the LX and the more upscale EX. The most noticeable difference is the second row of captain's chair seating in the EX.
With the second generation, the Odyssey took on many of the characteristics of American minivans, an obvious attempt to blend in better with the market. It was a smart move by Honda. They knew they had the best minivan, it was just a matter of getting the American people into it to experience the difference. That just happened to mean they needed to look similar to their counterparts.
The third generation, introduced in 2005, is still being made. If the Odyssey line is continued it will likely get an overhaul in 2010. The biggest upgrade on the 3rd gen Odysseys is the 3.5L V6 engine and an i-VTEC CVT transmission on the Touring and EX-L trim lines.
The Japanese models of these minivans have been significantly different than their American counterparts since the second generation.
If you are looking to buy one of these used, get in line. This seems to be the minivan that everybody wants to buy at a discount to full retail. They know about Honda's reliability, and they know a nice used Odyssey will probably last longer than a new Ford Freestar or whatever the heck they're calling their family hauler these days. I would suggest looking on eBay. The prices will be much lower than on your Honda dealer's certified used lot, and you're still getting a Honda.