One problem related to engine burning oil has been reported for the 1999 Honda Odyssey. The most recently reported issues are listed below.
The car seems to consume motor oil and I have to add motor oils after certain miles. I did oil level check every month or bi-monthly and I started to realize that I was driving the van with very low oil low level. At first I thought it could be because the car is old but from my experience with other much older car, oil consumption has not been an issue. Check with the dealer and other mechanics and they all gave me the same explanations that the issue is related to the mileage of the car (getting old). At the time I started to realize the issue, the car had only approximately 80k miles. . .