Psyshock is essentially a special move, but it's only unique since calculations are made by using the opponent's Def, in oppose to their SpDef. However, battle field conditions and Pokemon abilities are taken into consideration like any other SpAtk move.
That being said, if the opponent has Reflect in play (move resisting opponents Atk), Psystrike will ignore it, but it can't ignore Light Screen (move resisting opponents SpAtk). In concern to abilities, if the opponent has Weak Armor, it's ability will not activate since it needs to be hit by a physical move.
So overall, Psystrike uses the attacker's SpAtk, but the opponents Def.
Hope I helped! :)