Talcum powder is good for absorbing oil stains, I'd try and mop up as much of the oil stain using this before using a good degreasing agent (like an oven cleaner for example).
Baby wipes (not the lotion ones as they are oil based), get cheaper brands as they are are not lotion based and so should lift the baby oil. I successfully removed Sudo Creme that was gunged onto a wool carpet with baby wipes. Great for cleaning leather sofas too