A stupid person. 'idiot' describes someone that is stupid, but adding '-stick' denotes that the person is as dumb as a stick.
You missed the field goal? an 18-yard attempt?! Fuckin' idiotstick.
Its a person who is a complete idiot and drunk.
Its when a bartender typically in Souther California is blackout drunk trying to flare bartend with a half a watermelon on his head wearing it like a helmet dressed up in an Iowa fottball t-shirt. What an "idiotstick".