Welcome to Just Answer.
Sorry to hear about your problem.
I have heard that sprinkling baby powder right onto oil stains, covering completely and letting it sit overnight seemes to pull the stain out. The next morning brush off the excess powder and hand-wash the spots with a little bit of dish washing liquid and then hang it up to dry. The oil stains should be gone.
If you need further help or clarification on this answer, please do not hesitate to reply to this post.
Thanks for asking your question at Just Answer.
Best of Luck, Brian
Please leave feedback at your convenience.