Cleaning Rubber

I checked the memories and tried some of what I found, but nothing has worked and I need some guidance. I have a bag (http://www.amazon.com/Rubber-Chicken-Handbag-Pocketbook-Henbag/dp/B001G8N95I) which smells strongly. Amazon says it's made of rubber with nylon handles so I guess it's a rubber smell, and it's very strong and slightly nauseating. I tried rubbing the outside and inside of the bag with baking soda, then separately with vinegar, and I don't think they made a difference. I haven't put it outside to see if the smell will dissipate, because of the constant rain, but now it's started freezing every night instead maybe I should try that. I haven't tried spritzing it with vodka either because the only vodka in my house is expensive. What should I do?