My Honda Odessey starts on key but when you let the key go engine cuts out.

Replacing the ignition switch will solve your problem. Disconnect the negative battery cable, before beginning work.

Ignition Switch Replacement

1. Disconnect negative battery cable.

2. Remove dashboard lower cover and knee bolster.

3. Disconnect 5-P connector from under dash fuse box and 7-P connector from main wiring harness.

4. Remove steering column covers.

5. Insert key and turn it to "0".

6. Remove two screws from switch and replace.