I - Rules
(see AOD, p. 9)
A monster with the Morph ability can choose which dice it attacks with. For each morph die (indicated by a die icon with a question mark) the monster has on its reference card, the overlord player may choose a red, white, blue, yellow, or green die to roll, as limited by the dice that came with the game. The attack must include at least one red, white, or blue die, but can include more than one of those dice if so desired. The overlord also chooses what type of attack the creature makes (Melee, Ranged, or Magic). The attack must include a red die to be a Melee attack, a blue die to be a Ranged attack, or a white die to be a Magic attack.
Example: A chaos beast attacks a hero. It has 3 morph dice on its reference card, so the overlord chooses 3 dice. Taking a big risk, the overlord decides to roll 1 blue, 1 red, and 1 white die for the attack. Since he has used all three dice listed above, he could choose to make the attack Melee, Ranged, or Magic.
II - References
Heroes with the Morph ability: none.
Monsters with the Morph ability: Chaos Beasts.