If the transmission fluid hasn't been changed recently, you can try a fluid change, but I think it's more likely that the trans is on its last legs.  If the fluid looks burned, it might be worth it.  We had a 2005 Odyssey that had the problematic trans with design flaws.  Not sure if yours is the same trans, but when ours started acting up I started changing the fluid about two to three times a year and it bought us a couple of years before I had to have it rebuilt.  In my case the fluid turned black very quickly because it was not circulating properly through the trans cooler (again, design flaw).  Thankfully, it does have a drain plug :-).  Unfortunately, there is no trans fluid filter that is easily accessible without removing the trans.  Mine had to be rebuilt around 180K.

Try swapping in a new OEM 2nd gear pressure switch, and doing a 3x drain and fill with Valvoline Maxlife ATF, driving at least ten miles between each.