Actually, I second McGoo's suggestion to get professional advice. If nothing, NOTHING that you know how to do is working, then maybe a pro will have some techniques that would be appropriate for an older teen. No, not the cheesy parenting classes where they tell you to train a kid like you'd train a dog--that only works for very small children who aren't too bright. Talk to someone who is specifically experienced in dealing with troubled teenagers. At 18 and 16, could be rather late in the game, though--it's pretty hard to change attitudes and behaviors when they've been ingrained for so long. And then in the event that Child & Family Services gets an unpleasant phone call, you have the pshrink backing you up.
For those that admitted they were out of control as teens, if your parents had said, you have to make your own food, don't have to clean, can cuss us out, etc; would you have changed your patterns?
Since you asked...I did have to make my own food, earn my own money, buy my own clothes, do my own laundry, etc. from age 15-18. I moved out sorta-kinda (lived with friends and boyfriends off-and-on) at 17, permanently at 18. And I still cussed out my mother when we fought, and we fought incessantly. She could say nothing right to me, I could say nothing right to her, and that was that--honestly, I don't think she really wanted to be a parent in the first place, and probably should not have had children. We have completely opposite personalities, even as adults.
But WRT behavioral issues such as being just basically civil, my mother went the "professional help" route and shipped me off to an all-girls' boarding school. Their punishments were, as you say, non-negotiable and simple: getting up at 7am on a Saturday to do homework, having to schedule extra classes during periods when good kids got free time, having "town visiting" and entertainment privileges (trips to the mall, dances with all-boys' schools, etc.) revoked. They worked because they were simple and consistent. They told you exactly what you were expected to do, in no uncertain terms, and if you did it all was peaceful in the world, and if you were bad you would be up at 7am in uniform, working on extra geometry problems.
I think it really does help to know where your parenting skills end and when it's time to call in the pros. I really do. I watched my father-in-law struggle endlessly, taking years off his life, trying to parent his out-of-control and wily step-daughter. I told him to consult a pro or send her to boarding school, he got mad and did the "how dare you tell me how to parent my kid!" act. Sure enough, as a teenager she was pregnant twice, used drugs, drank, stole from her parents, made a general nuisance of herself and the nicest thing I can say about her today is, "at least she managed to hold on to her job at Taco Bell." She's not a good kid. And now she is far too old to get her mouth washed out with soap, so she's stuck that way.
Your mileage may vary and all that.