You can't cook without at least getting hit by oil sputters from time to time. Oil stains on your clothes can be annoying. But if you act quickly, they won't stay on.
Food52 has a neat trick to remove them with simple kitchen ingredients like baking soda and a bit of dishwashing liquid.
Just sprinkle powder on the stain (flour, baking soda, or baby powder), then tap it into the stain and let it sit to absorb. Brush off the excess before applying dishwashing liquid directly on the stain and dab it in (don't rub in). Launder it in the warmest water advised for that particular fiber your linens are made of.
If the stain is still there, repeat the process.