You can escape your opponents attacks by doing the following as soon you see your opponent start his move(time it so that you perform your escape when you see your opponents move pause, before they start swinging towards you. You have a better chance for success if you do the escape for the same move your opponent is doing to you (Playstation this is necessary), but the Up or Down ones seem to work on all the knockback attacks(Saturn only). (note: Where it says to "hold" the Block button, on the Playstation version you must "Tap" the block button and the direction at the same time)

Hold Block and press Up=best escape from Up+Attack(attack that would knock you into air)
Hold Block and press Down=best escape from Down+Attack(Attack that knocks you downward)
Hold Block and press Forward=best escape from Back, Forward+Attack (across screen attack)

To escape from the grab and attack portion of a combo, double tap the control pad any direction except straight up or down while Holding the power up button.