Leech: Parasite can use Steal Energy.

Attack Drain: Give Parasite a power action. As a free action he can use any standard or named attack power possessed by an opposing character 4 or fewer squares away to which he has a clear line of fire; he has a range value of 6 for purposes of using the attack power. Parasite can use the power until he loses Attack Drain, Attack Drain is countered, or he uses Attack Drain to use a different power. After the resolution of an action in which Parasite uses a power via Attack Drain, roll 2d6. on a result of 2-5, dealt Parasite 1 penetrating damage.

Defense Drain: When Parasite is given a power action, as a free action he can use any standard or named defense power possessed by an opposing character 4 or fewer squares away to which he has a clear line of fire. Parasite can use the power until he loses Defense Drain, Defense Drain is countered, or he uses Defense Drain to use a different power. After the resolution of an action in which Parasite uses a power via Defense Drain, roll 2d6. On a result of 2-5, deal Parasite 1 penetrating damage.

Brain Drain: If an opposing character 4 or fewer squares away to which Parasite has a clear line of fire has an action token, Parasite can use perplex, but he can modify only his own combat values.

If Parasite uses Attack Drain to use Super Strength, when exactly would he roll for the potential penetrating damage? When he picks up an object, when he's holding the object and moving around the map? When he uses the object in an attack?
Parasite would roll for the penetraing damage after the resolution of an action during which he either picked up an object or attacked with an object. Simply holding the object will not activate the roll off.

I see that the wording for Attack Drain and Defense Drain is slightly different. Attack Drain begins with "Give Parasite a power action" while Defense Drain begins with "When Parasite is given a power action." What does this difference mean?
Parasite must be given a power action expressly for using Attack Drain. You would declare during your turn, "I am giving Parasite a power action to use Attack Drain. I will use X's attack power Y." Or something along those lines.

Meanwhile, because of that phrase "When given", Defense Drain can be used anytime Parasite is given a power action to do anything. The power action given to activate Attack Drain would work, letting Parasite get both an attack and defense power with one action. Alternatively, if Parasite was given a power action to use Charge, he could also activate Defense Drain when he Charges. Or any other power action (maybe he's got Smoke Cloud after using Attack Drain in an earlier turn and he's laying down some cover).

Parasite may not be given a power just to use Defense Drain, though. The power action has to come from something else.