One problem related to oil pump has been reported for the 2010 Honda Odyssey. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2010 Honda Odyssey based on all problems reported for the 2010 Odyssey.
Engine light and using oil. Codes p3497 and p3400. Engine oil pump outputs high oil pressure causing cylinder pause mode. Vehicle in motion. Same problem as service bulletin 13-055 with 2013 Odyssey.