Hey ssgt, welcome. (is that staff sergeant)
Couple of things, an old oil finish might contain lead, so take precautions. Does the old finish have a sheen and are you looking to put a sheen on again? If you prefer a flat finish the likelihood of finding a flat oil finish these days is pretty slim.
To prepare I would take a thin flexible six inch spacle blade and work it between the old finish and the peeling coat, holding it close to parallel to the ceiling. Carefully scrape until the edges seem tight.
I would then apply a coat of Zinsser oil based primer sealer to the exposed areas. The oil Zinsser will create a bond to the old finish without sanding and lock down the loose paint edges.
Then apply skim coats of joint compound over the edges to feather them out. If you have large areas of exposed old finish, you don't have to cover all of that if it's not damaged, just concentrate on feathering the edges. Lightly sand the compound with 220 sandpaper.
Personally, I would then use the rest of the cover stain and apply a full coat of primer to the whole ceiling.
Finish with a quality latex finish.