Four Mamodo teams can only be unlocked by purchasing cards in the Bonus mode.
Sometime in Zatch's Story Mode you will fight Kido/Doctor Riddles after you fight him go back to the Main Menu and it should unlock the Password Screen, then use the code listed to Unlock 20 Random Cards and 300 points.
NOTE: This code can only be used once.
Buy cards (using the points you have gathered) in Omage mode. By obtaining certain cards will unlock new stages and secret characters.