hi there
two things
first,
scratches, what is scratched ? if its stainless then wet and dry in the direction of the stainless grain, takes a long time and practice,
if its coated then you need a plastic surgeon
in fact the plastic surgeon will do both, and does it very well
secondly
instead of using baby oil, use a stainless steel plish, something like clover chemicals dazzle. its great. and wont become sticky. you will be totally lown away with the results.
regards
martin