Thank you! That looks like a very helpful link!You should have a new key cut as a backup spare. Do you have any spare keys?
Perhaps buy a FOB. 2001-2004 Honda Odyssey 5-Button Key Fob Remote (OUCG8D-440H-A, 72147-S0X-A02)
No experience with the above link, Just giving an example.
Lubricate the door locks with a good lock lubricant.
Perhaps work on repairing the rear hatch lock. It maybe that the rod fell off the key lock. Not too hard to access. Use youtube vids.
If the hatch unlocks with the unlock on the doors, it will probably unlock with a FOB.
Buffalo4