I think that I always knew that this term referred to being drunk. But to-day I learnt something new about sheets. I am NOT a sailor and my knowledge of the sea has been mainly gained from reading books. In one of his poems Robert Louis Stevenson he called "Christmas At Sea" he says "The sheets were frozen hard, and they cut the naked hand" so , I thought that the sheets must be the sails. Not so. Wikipedia says it is a rope.
But then I read further and it says, the corner of the sail. J.T.