I've had this same problem on my 2000 Odyssey starting at about 25k miles. The first time I took it in to the dealer, they said there were carbon deposits on the accelerator cable. I never could get a good explanation on how you can have carbon deposits on the accelerator cable but they cleaned it and it got better - for a few weeks. We took it back in the second time and they re-cleaned the cable and also the throttle body. Again, it got better - for a few weeks. The third time we took it in, they re-re-cleaned the cable and adjusted it to hopefully eliminate any binding that might be happening. This worked for a few more weeks until we went back in for a fourth visit. This time, they replace the entire accelerator cable and re-cleaned the throttle body. Once again, this worked for about a month. Of course by this time the warranty had expired ( > 36k miles ). Luckily, since we had so much "documented" troubles with this, the fifth and last time we took it in, they replaced the entire throttle body without any charge to us. We are currently going on five months without any sticky accelerator problems.
I've talked to two other Odyssey owners in the Houston area that have had the same issue with their 2000 models. The first had the accelerator cable replaced and the problem went away. The 2nd person, I just talked to last week and they were just starting to have the issue.
Before they replaced the throttle body on our last visit to the dealer, we had the service tech and the service manager drive our Odyssey and 2 others that were in for some other service. Both of them said my wife and I must have really strong legs because the accelerator on our Odyssey was so much harder to push than the “normal” Odysseys.
If you are still having this problem, have your dealer replace either or both of these parts as soon as possible. Cleaning will just mask the problem until the warranty expires and then you might have to pay the repair cost yourself.
Good luck.....