What are some waterproof materials that meet my criteria for folding origami stars and cranes eggs?
You could try using palm fronds, which can be woven to make beautiful stars and patterns:





For more details about the craft of palm weaving, see this question and the links given in its answer (disclaimer: answer posted by me).

They're obviously waterproof, since they come from plants which are naturally found in wet conditions. They come in long strips, which are (perhaps surprisingly) pliable enough to be folded into intricate shapes but also strong and tough enough to stay in shape. They should be inexpensive, at least if you're living in the right region (e.g. somewhere there's a strong Catholic community with a tradition of palm-weaving). The only criterion they don't meet is being able to come in multiple colours, but it might be possible to paint the palm fronds before folding them, if you can find a paint that works well on organic material like this.