I have a 2002 Oddy, it has been a great minivan for the wife and kids - far, far, FAR superior to the miserable POS Suburban and Jeep Cherokee that came before it.
They did have transmission issues early on in the 2001-2002 timeframe due to insufficient lubrication of a couple of the gears in the auto transmission. This was solved as mentioned above by installation of extra jets / nozzles to direct ATF to the right spot. When you took the Oddy in for the recall, they looked at the gears to see if there was heat-related discoloration of the metal, and if so they replaced the transmission. If the gears looked OK, they installed the new nozzles and extended the warranty on the transmission to 100K miles.
We had the fix done on ours shortly after the recall began. It was a no-muss, no fuss operation - took it in that morning, had it back that afternoon. In the 80K miles we've put on it, we've had only one transmission issue and that was the recent failure of a sensor. The Oddy transmission will indicate problems by flashing the Drive indicator light, ours started blinking so we took it in and they hooked up the computer and diagnosed the issue quickly. They replaced the sensor and the van was ready just a few hours after we dropped it off.
The Oddy has a great engine, it is the Honda V-TEC and the minivan will really get up and go. It gets about 26 mpg average in highway driving, but around town with the wife's soccer mom type activities it usually returns about 17 mpg.
The handling of the van is extremely good, it has a taut suspension and very good road feel. That unfortunately translates into road noise, the only real complaint I have found on the Oddy. That improved when we went to Cooper tires but it is still an annoyance. Considering that is the only complaint we have, the van must be doing pretty good. By the way the road noise leads some to upgrade the stereo, the stock unit is very nice but doesn't have a huge amount of power.
Our repairs to date:
- transmission nozzle installation (recall)
- Replaced torn motor mount (rip in the isolator)
Other than that, only service has been oil changes and scheduled maintenance.
I'd buy the van again in a heartbeat, about the best vehicle we have ever owned. You can get a very nice used one in the year range you listed for a very good price now, and it will have a long and useful life ahead of it.
Highly recommended.