One problem related to starter relay 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.
Van will start periodically. But the next day the battery will be dead & has been jumped off with jump box & other vehicles assist. But battery is new, terminals cleaned. Van will not even make a clicking sound. I feel that there is evidence of faulty ignition switch, starter relay or parked/neutral safety switch & maybe more depending on chassis electrical. The vehicle is also stationary until the next morning. This happens to be my wife's vehicle. . . Need this fixed ASAP. .