The correct answer is option 3: Homothermy.

Homothermy refers to the ability of an animal to maintain a constant body temperature regardless of the external environment. In this case, all three animals mentioned, parrot, platypus, and kangaroo, are homothermic, meaning they can regulate their body temperature.

Option 1, Oviparity, refers to the reproductive method where animals lay eggs. While some birds, like parrots, are oviparous, both platypus and kangaroo give birth to live young, so this option is not common among all three animals.

Option 2, Toothless jaws, is not a common characteristic as parrots have toothless beaks, but both platypus and kangaroo have teeth.

Option 4, Functional postanal tail, is only present in kangaroos. Kangaroos have a muscular tail that helps them balance and jump, while neither parrots nor platypus have this characteristic.

Therefore, the common characteristic among all three animals is homothermy, as they can regulate their body temperature.