There are kits super cheap on eBay. It’s a few steps but works for a while. The toothpaste recommendation is a waste of your time.
Leave it to the "lowly" plain, white toothpaste to come to the rescue. :) According to this article, it's the best way to remove that oxidation. Wishing you the best.
White toothpaste and buff off. You might want to get an attachment for your drill to buff them.
There is no 'perfect' solution. I use the toothpaste routine, but I also start with rougher 'red' ScotchBrite scrub pad, then use the gentle 'green' pad, then use a t-shirt with toothpaste. Scrub well with that toothpaste and then buff with a cotton wheel on your drill. MAKE SURE you wax well and often once you get your lights clear again or they'll oxidize again really quickly because you will no longer have any protection on the plastic.