Can't promise it will work, but some models will reset the alarm if you use the key to open the rear hatch area or the passenger side door. May sound silly, but it's worth a try - even if it's already unlocked, put the key in and turn it to unlock that cylinder - this may activate the shut off for the alarm and allow you to start the car. If not, search through your owners manual (if you have one) for clues ... otherwise you're stuck towing it to a dealership :-(
RepairPal Certified shops can diagnose and repair your 2001 Honda Odyssey. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.