One problem related to power steering fluid has been reported for the 2008 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2008 Honda Odyssey based on all problems reported for the 2008 Odyssey.
Issue with power steering rack and pinion leak. As part of power train, the rack and pinion leak creates safety issue while driving. Turning effects driving and pings, knocks are heard @ 52,000 miles. We have lifetime unlimited miles and years warranty from dealer. Warranty company and dealership parted ways so brandon Honda verbally refuses to fix problem. This should be a recall. Other Odyssey owners with this issue. Since it's not a recall, dealer should fix under our warranty. While sitting, power steering fluid leaks from rack and pinion. Seals/gaskets, whatever else reason for leak which is expensive to fix. We replaced a cv joint at our expense this year. All the steering and powertrain parts are listed under powertrain on Honda website's parts page.