I personally think three year olds can be much harder than two year olds, and there's nobody who can push your buttons like your own child. First off, the mouthing behavior is unusual at his age if he's not getting any teeth, so this is probably sensation seeking behavior. If he's drooling a lot, he may have low muscle tone in his mouth (hypotonia) which could also cause unclear speech and feeding problems (gagging etc.). Your pediatrician can refer you to a speech language pathologist or occupational therapist who can help. If he's craving the sensation of chewing, get some things that it is safe for him to chew and try to steer him towards using those. You can order a products online that are safe to chew (one of which is called a chewy tube http://www.rehabilitystores.com/For-Kids/).
The greater behavioral issue is harder, but you can get yourself out of this power struggle rut. First off, it is so important that you do not spank him. Spanking and other forms of corporal punishment have been studied for decades. The research data shows that spanking makes children more aggressive, more defiant, and more likely to get physical with peers (and parents!). Though a spanking will stop the behavior in the moment, it will make the situation far worse over time. Over relying on bribes and distraction will also work in the short term, but make your life harder as time goes by. The most effective way to change behavior for the long haul is to systematically teach your child new ways of behaving.
Check out the book The Kazdin Method by Alan Kazdin for great advice in managing power struggles effectively. Improving your communication with your son will also help, so I recommend How to Talk so Kids will Listen and Listen so Kids will Talk. This book will help you reduce the number of power struggles greatly. The best advice I can give you is to go see a psychotherapist for parenting help. Ask for parent management training, parent effectiveness training or parent guidance. Most of the therapists time should be spent with you, teaching you how to get the results you want and strengthen your relationship with you son.