Is there any way to help a Power do tasks that isn't your power?

Not Directly, but yes

First off, Powers really aren't allied to any other Powers. Even if both Powers are part of the same major faction, they're also acting against each other. Being allied to the same major faction simply limits what you do against the other power. You should probably just stick with helping out your own power and undermining all the other ones.

Things you can do to help a Power, without being pledged to that Power:

• In a system where they are being undermined, destroy player ships that are doing the undermining. I don't think killing NPCs will help here.
• Flip systems from minor factions the power is weak against to minor factions the power is strong with. If an opposing power is trying to prep the same system (or one with competing control radius), help out faction types the opposing power is weak with. The primary prep/expansion/control systems are most important, but anything in the control radius will help. The Command Capital (CC) cost of systems is lowered when the controlling faction government type is one the Power is strong against, and the cost increases when it's a type the Power is weak against.
• In the various forums (Frontier's own, reddit, any specific to groups backing your power), convince players to have a truce between the powers, so that players pledged to your power aren't undermining the "allied" power.

That's all I can think of, but there may be other indirect ways to help an "allied" power out.