What is your most reliable method for removing oily stains from your table linens?

True Pegeen. However I have never had anything bleed. Just lucky, I guess but you are right about that.

About the Scotchguard possibly causing dye to bleed... I speak from sorry experience. Not all fabric dyes are created equally.

Nataliesztern, just a note that not all fabrics are Scotchguard safe. It may cause some dyes to bleed. The can of Scotchguard will caution you to test a small sample of the fabric in an inconspicuous spot to be sure.

To begin with I spray everything new with Scotchguard. Especially table linen including linen napkins. As well I spary all my clothes.

Thank you, everyone! I really appreciate your time and expertise.

Creamtea's process works. I've also tried some of these from Martha Stewart's stain removal chart:
http://images.marthastewart.com/images/content/web/pdfs/pdf3/stain_removal_basics.pdf

I sprinkle powder on the stain (flour, baking soda, or baby powder). Tap it into the stain and let it sit to absorb. Brush off, then apply Dawn dishwashing liquid directly to the stain and dab (don't rub) that in. Launder in the warmest water allowable for the particular fiber that your linens are made of.