Pour baking soda over the oil stain on your silk sofa upholstery. Cover the stain completely. Allow the baking soda to sit on the upholstery for 20 minutes to absorb oil and odor.
Remove the baking soda and absorbed oil with a hand vacuum.
Moisten a sponge with dry cleaning solvent. Remove excess moisture by squeezing the sponge so it's merely damp, not wet.
Dab the remaining oil stain on the silk sofa with the dry cleaning solvent. Add more dry cleaning solvent to the sponge as needed.
Press a dry cloth into the silk fabric to absorb the solvent.
Hold a hair dryer about a foot away from the surface of the silk upholstery. Set the dryer on the lowest heat setting and move it back and forth over the silk upholstery until the fabric is dry.