If as piatkow has answered you want to run CJ and Adsense ads on the same page, you are absolutely fine to do that.
The rules surrounding Adsense are less stringent. You can have up to 3 ad blocks and some site links, in addition to other advertising. There are some issues with other contextual traffic sources like Chitika and Kontera, but CJ and Adsense is fine.
As far as Adwords sending traffic to CJ directly, you might be OK, you might not, it really depends on the merchant you promoting using Adwords themselves or not.