Unlimited money
Hold L2 + R2 and press Left(2), Right(2), Square(2), Circle(2) at the car and item selection screen. A sound will confirm correct code entry.
Unlimited nitros
Pause game play, then hold R1 + R2 and press Down(3), Circle(3).
Invincibility
Hold R1 + R2 and press Up, Left, Right, Down, Triangle, Circle, X at the options menu.