Yep. I think now it's called "vinyl tablecloth", but that's the idea yeah. Cotton on one side for durability (so it doesn't rip easily like a regular sheet of plastic would), some kind of plastic on the other side to make it waterproof (unlike regular cotton tablecloth which gets wet/dirty).
Not at all. Contemporary oilcloth isn’t impregnated with oils anymore like it has been in the past, it just kept the name. Now it’s just cotton with a vinyl backing on one side. And it’s not like they’ll be eating it… It’s very tough and holds up great, and will be under the bedding anyway.
I have oilcloth stapled to the floor of my coop, to protect the wood and to make the biennial big clean out easier. It's cheap, waterproof and durable, and very easy to install - cuts like fabric with regular scissors. Highly recommend, would solve the problem in your case. You can get it on...