Whenever Oracle's dial is spun via a power action, the Agent that currently has a power loses it (the power) and the Agent that was given a power action to spin the dial gains the new power. This may be the same Agent or a different one. Either way, you can not have two powers from Oracle's dial at once (either two different powers or two duplicate powers); the spinning of the dial negates the previous power.

my question is more of: does the agent keep the power until another agent makes the power action, or does is wear off after a turn?

Nowhere on the ICWO card does it say that the powers 'wear off'. The power is kept by the Agent until it is either KO'd or another power action is given to spin the dial.

but, whenyou turn the dial to grant another agent a power from her. the orinally agent loseing the poer that she had granted them right?

yes. And I believe that even if you move the dial 0 turns, it is still considered tobe moved and the first agent loses the power.

Correct.