I'm assuming the Meguiar's polish you've been using is #2 Fine Cut in the tan bottle? If so, that product is formulated to be used with a high speed rotary polisher, not by hand or orbital buffer. The haze you are seeing was probably caused by the abrasives in the polish not being broken down fully when used by hand. More polishing with #2 will only make the problem worse. It has nothing to do with oils.
Just like sanding, you remove large scratches by using a polish that produces small scratches. An orbital buffer with a med-light polish will help a lot, IMO. It'll take a good bit of effort to do this work by hand but it can be done. The 3M Swirl Mark Remover is quite a bit milder than the Fine Cut Cleaner so I'd recommend using that if you already have it.
You can follow up with a glaze which is mostly fillers and oils designed to hide very minor swirl marks and looks very good on black. 3M, Mothers and Meguiars sell nice glaze products at auto parts stores. Finish off with a quality wax and you'll be done.
Unless your paint is moderately oxidized or you need to polish out specific problem areas, I'd recommend retiring the #2 for now. You can always go back to it if you ever decide to start polishing paint by machine.
