It sounds like you are dealing with a rope worm problem. Like you have experienced, one of the tell tale signs is the horrid smell associated with these things. I can tell when I have expelled some without even looking just by the smell.
I have taken over 600 pictures of what has come out of me. The picture I referenced here is just one that looks similar to what you posted. I have had some snake skin looking things like you have posted but not near like the volume of the rope worm material that has come out in all kinds of shapes and stages.
Charlie.