Zeke is a skeleton:
Hold X + Circle + Square + Triangle at the opening sequence. Release the buttons at the title screen.

Zeke is invisible:
Hold X + Square + L1 + R1 at the opening sequence. Release the buttons at the title screen.

Invincibility:
Hold Right, then press Square, Circle, Circle, Circle, Square, Circle, Triangle, X during the game.

Weapon upgrade:
Hold Right, then press Square, Square, Triangle, Triangle, Circle, Circle, Circle, X during the game.

Level select:
Hold Right, then press Circle, Circle, Square, Triangle, Triangle, Square, Circle, X during the game.