How to remove olive oil stains from cotton/wool cloths

For hard, chemical-resistant surfaces such as marble, bleach or peroxide cleaners will help. On things like counters, pots and pans, a Magic Eraser will often take off the stain. Sometimes a harsher abrasive like Comet or Barkeep's Friend will be needed.

Softer or porous materials, including cloth and many plastics often CANNOT BE UNSTAINED. In my kitchen we treat turmeric like a dangerous chemical -- isolate, contain, and plan ahead to limit exposure. It's just that destructive.

You might as well tie-dye or bleach white any clothing you get turmeric on; it India it is used as a dye for saris because it will semi-permanently tint cloth. You can brush off the dry powder harmessly, but when it is moistened and allowed to sit for a moment, the color is pretty much permanent.

Edit: UV+peroxide: I saw a patent for removing turmeric stains from upholstery using UV light and hydrogen peroxide. You might try soaking fabrics in peroxide or Oxyclean (which uses peroxide) and leaving then out in the sun. Can't hurt right?

Edit: strategies to manage turmeric without making a mess

1. Plan ahead where you'll use it, and which utensils and vessels will hold it, so you don't mess up anything you don't need to.
2. Re-use already turmeric-stained items so you don't wreck anything new
3. Mortars and pestles, tupperware, wooden and soft plastic utensils are a lost cause. At least the stain is purely cosmetic?
4. ALWAYS ALWAYS ALWAYS wear an apron.
5. Keep spilt powder dry (it won't stain) and brush it off with a paper towel into the garbage. Brushing away promptly keeps you from inadvertently spilling liquid on it, or wiping it with a wet towel during cleanup. That is, unless you want a neon-green counter and towel?
6. Whenever you spill something containing turmeric, promptly wipe it off, to reduce staining.
7. Hard ceramic and porcelain are immune to staining unless the surface is rough. Try to use these for storage. Glass will stain. Stainless steel is resistant but not immune.

With these strategies, I find I can use turmeric regularly without problems.

I use bleach to remove mold and mildew stains from my bathroom and while the process would be gross, I would think that once thoroughly washed the bleach wouldn't cause any harmful effects to the pan or to future snacking humans.