A trick thats worked for me in the past has been to buff the plastic by hand using a long strip of cotton t-shirt and car wax. Similar to polishing alloy hubs, the wrapped cotton strip usually does wonders. Armor All, Vaseline or other liquids that aren't too abrasive would probably work as well.

I have also done this numerous times to chalky, oxidized, black painted mtb bars with excellent results. WD-40 works well on the bars, but I would be hesitant to use it on plastic bits for fear of breaking down the plastic.