I'd like to start hanging out my laundry again. There is a laundry line on my back porch, but I haven't used it in years. I suspect that if I don't clean it somehow before using it, I could end up with marks on my clean clothes.
Honestly, I'd just replace it. Nothing worse than hanging out clean clothes, and having them come in stained! I buy my line at the dollar store. I get the nylon coated wire, so I can easily wipe it down.
Run a hot soapy wash cloth over it and then a clean one to "rinse". If the wash one is very dirty run it over a shorter distance, rinse, and re-do.
We used to have a metal wire clothes line. We just ran a rag over the wire until clean and hang em up. Worked good. No marks. If its real dirty just use a cleaner first, then it should be ready to use.
My suggestion to would be to replace it as it might be more trouble than it's worth to try to clean the old one.