My character's strength is normally 20. I had the feat Power Attack. My strength dropped to 6 due to poison.
Does that mean I no longer can use Power Attack until I regain my strength?
From Feat Prerequsites:
Some feats have prerequisites. Your character must have the indicated ability score, class feature, feat, skill, base attack bonus, or other quality designated in order to select or use that feat. A character can gain a feat at the same level at which he gains the prerequisite.
You must meet the prerequisites in order to use any feat. If something reduces your Strength below 13, you cannot use Power Attack. You still have the feat (for example, if you have Cornugon Smash which requires Power Attack, but does not independently require Strength 13, you could still use it).
However, as pointed out by ShadowKras’s answer, ability damage, as from poison, does not actually reduce your Strength.
No. Don't re-calculate anything on your character sheet if you take ability damage. Poisons cause ability damage.
Ability damage does not actually reduce your ability score in pathfinder, you simply take some penalties related to that ability. Just as temporary ability increases are not enough to satisfy feat requeriments (a magic item must be worn for 24 hours before the bonuses become "permanent"). These penalties are every 2 points of ability damage taken and will affect some stats related to that ability, like reducing your attack bonus and damage if you take STR damage, but your carrying capacity and actual STR is unaffected.
If you take ability damage on your INT score, your spell DCs are reduced by 1 per 2 damage taken, and you take -1 on int-based skill checks, meaning that anything else related to INT stays the same, such as 3+INT uses per day abilities from a wizard's school.
Ability Drain, on the other hand, does reduce it. That is because ability drain is permanent until healed by spells, while ability damage can be recovered over time with rest.
Poison is ability damage, not ability drain, unless specified otherwise on the poison's description.
If you check the description about ability damage on constitution, you will notice that your current and max hit points go down, so it's an exception in this aspect.