I've had great success with using dishwashing liquid to get grease and oil stains out, especially fresh ones and even reducing the damage of set in and old ones.   Just dab some in and set aside until ready to wash!  If it's really bad I even throw a little of dishwashing liquid in the wash with the garment.

 I also tried shampoo as suggested on Teh Internets but that didn't work out so well.  

 I will try your baby powder trick !