ぽあー is a coined onomatopoeia so I can't tell for certain, but I think it's same as ぽけー or ぼけー.
Gawking, spaced-out,dazed, vacant mind, brainles, or like those.
ポン is the equivalent for "phut" or the sound effect for popping up. It shows someone hitting on a idea when it's used with an electric bulb figure.