A portmanteau of 'stroke' and 'pout'. A term used to describe the facial expression that forms a sideways pout with attitude, using only a side of one's face...hence stroke.
Girl 1 to Girl 2: You know that moment you're with a hot guy and he says something that makes you snarl, but at the same time you want to do unspeakably filthy things to him.....that's when you pull out the strout.
Man, that chick has so much attitude, look at her strouting.