In all the time I've spent near the ocean, I've never seen anything like these. They looked and felt like bits of vinyl shower curtain, but I think they are creatures. They just appeared one day on the beach and there were loads of them in varying states of decay. Last year, there were hundreds of large red jellyfish washed up one day; this year it's the little jelly things.
If anyone knows what they are, send me an email.
Update: The mystery is solved: my friend S tells me they are Sail Jellyfish or Velella velella. It is fitting that such strange things should have such a strange name.