Mother Mosquito 

Go to the character selection screen and hold L1 and press Up, Right, Left, Down, Square(2), R1(3). You should hear a shout if entered properly.

Father Mosquito 

First enter the Mother Mosquito code. At the character selection screen then, hold L2 and press Up, Right, Left, Down, Square(2), R2(3) You should hear a shout if entered properly.

Two player mini-game 

Press and hold start+Select right after booting the PS2 (after turning on). 

Controls
Square to move forward
X to jump
Triangle to do a super attack