@User I'll drop this here, for train tickets from Copenhagen (Københavns Lufthavn for departing from the airport or København H for departing from central station) to Odense St.: https://www.dsb.dk/en/
If you can get Orange tickets, they're the cheapest, but you have to take them at the exact time you book them for. Other tickets are valid all day, so if your flight is delayed you just take a later train.
Make sure to book seats! And you're allowed to kindly tell a person who might be in your seat: sorry, I believe I reserved this one. Danes will usually get all flustered and apologize that they took your reserved seat 😉