One problem related to gas recirculation valve (egr valve) has been reported for the 2004 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2004 Honda Odyssey based on all problems reported for the 2004 Odyssey.
Bought the Honda in may 2004. Noticed a slight hesitation at times when engine was not warmed up. I complained about it in my new car survey form and each time it was serviced. On 8-5-05 they replaced egr valve, as it sometimes would cause this failure. On 2-5-07 it totally quit as I was starting a turn into pep boys parking lot, if anyone would have been coming out I would have run into them as I had no steering nor brakes. Took it into the dealer and said I wanted it fixed before I would have an accident. I had mentioned something about the lemon law and they said I would have to contact Honda of America, which I did. End result was dealer took car for three days in March 2007. They tested it but could not make it fail so nothing was done. Both Honda of America and the dealer gave me their final comment: if they can't see a failure there is nothing they can do for it.