the Odyssey battery/alt/starter system is a tricky system to diagnose. Most point to the alternator being the problem most of the time.
What year is your Van and how many miles?
My 2011 has 120k on it and I had to replace the alternator a couple months ago. Some on the forum have had theirs go bad within 70k, but that's not typical.
If you do end up getting a new alternator get the Denso remanufactured unit... lots of problems with other brands. Denso is the OEM manufacture