What is the best way to get the oxidation off my clear coat?

Turtle Wax used to make a fine buffing compound and wax combination.  It takes elbow grease but you can do it by hand.  Just follow directions on can or bottle. Use clean cloth rags(no zippers or buttons or dirty)meaning washing it clean first.  Personally I have not seen oxidation on clear coat.  Most likely your car needs a good car wash with soapy water(that does NOT come out of a well)  I have seen oxidized Red, dark green and black.  You are not in a rush to go anywhere so do it section by section. IF there is oxidation, that will come off, so will tar and road oil, and bugs.  She will be slick when you are done.

. This does not work on tires, use tire black there. and chrome polish for the chrome.

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. I forgot, there is no chrome.  It is all painted plastic.

Try buffing it with a polish and power buffer - (or have it buffed - a good car detailer will tell you if it can be repaired with some buffing and compound or polish.

A really good wax job.   

That damage is permanent and the only remedy is to remove the damaged clearcoat and re-coat the area.