Use a little old fashioned windex with a VERY CLEAN and VERY SOFT cotton cloth.

If it's chemical residue, then you need to be careful.

First, I'd wash the plastic with a soft soap (like MCGuire's boat wash -- a redish solution) and warm water. You can use a VERY, VERY Soft, CLEAN RAG.

I've used some McGuire's plastic cleaning spray bottles with some alcohol in them -- but old fashioned (vinegar containing) Windex seems to work best for me.

I don't use it all that often.

Then if you want to wax them, you can try that -- but I think you can do more damage by waxing.