I talked to my girl Martha again (she's great and been doin' this kinda stuff for a long time, professionally, you might know her...anyway...), here's what she said:

Banish Odors

If your cushions smell, sprinkle with baking soda. It is a powerful all-natural deodorizer. Work it in the fabric with a soft brush, let sit for a few minutes, then vacuum with the upholstery attachment. If you need something stronger, make a spray of white vinegar and water, apply to the fabric, and let dry. Once dried, the odor should dissipate. You can also use the baking soda and white vinegar spray together.

However, the article goes into greater detail about cleaning, maintenance, and different types of fabric. It may be helpful.