They all turn, Delrin Nylon, HDPE or whatever that HD?? alphabet is, sharp chisels, stop and clear the "plastic" strings that you will create. My experience is mostly with Delrin, work it like it is wood, but I prefer to wet sand using cheap auto transmission fluid from the dollar stores. I sand up to about 800 grit and then buff. You will NOT GET A HIGH POLISH SHINE, more of a matt looking finish. Buffing will improve the look. But buff at a slower speed with not much pressure or it can cause it to sort of melt the stuff. My experience is more with Delrin, not really sure on the others, as it has been a few years since I used any of them.
Nylon and HDPE? I have turned it. Mostly for some special type of tooling, usually I did not finish on it. Of the 2, I liked HDPE, but I think I thought Nylon sucked, but don't remember why.