Hi S.!
You really do have your hands full! Don't worry, you and your children will be just fine!!!
First, you have to know that girls at the ages of 8 and 9 are very egocentric. Studies have shown that 8 and 9 year old girls truly believe the world revolves around them, which is ok but will need strict guidance so that they are able to mature out of that stage. Your four year old is in her mimmicking stage so you'll have to set consequences for your older daughters and make sure your younger daughter sees them being reprimanded so that she understands that their behavior is not the acceptable one.
I have three children and my daughter is 9. I know it's hard to try and discipline when there are so many other household and familial "things" to tend to but just retrain yourself to be able to "drop" what you are doing and make sure you follow through with your discipline. When my daughter defies me, I simply tell her she has to go to her room for 10 minutes because she is "not allowed to treat me that way". Yes, you will probably get the tantrum and the screaming but bear with it and eventually you'll just have a stomping to the room result. It takes time but it will eventually work. And you will get the repeated "I'm sorry!!"; "I said I was sorry!!!", but just hold fast and follow through with the consequence/discipline of the 10 minutes in her room. I know it doesn't sound like a lot of time but it does diffuse any anger and frustration and you'll be able to talk to her afterward and explain to her how her defiance, rudeness, disrespect, etc. hurts your feelings and ask her how it makes her feel speaking to you in such a manner. Just be calm and patient and know that results are not immediate.
As far as your 16 year old, I would do the same but his consequences should be much harsher, such as no car or even worse, no going out on the weekend. Yes, you'll have a very angry boy on your hands but simply say, "go to your room for 20 minutes and when YOU feel you are calm enough to speak to me in an adult manner, come out and we can talk about the situation". This way, you are giving him the responsibility of calming himself down and deciding when he is ready to talk. He will also come to realize that he is responsible for himself, which will make him feel "more adultlike" and make it easier for you because he will be able to view you as his parent and not his "mommy", who is expected to do everything for him. I say this because I have a friend who has a 16 yr old son and she says she treats him like an adult but when he does anything he isn't supposed to, he knows there are consequences and "mommy" must step in.
There are many links to research and get answers from. I found a few to get you started:
http://www.dltk-kids.com/articles/behaviour.htm
http://www.siue.edu/~jejewel/Defiant%20children.html
http://www.crisiscounseling.com/Articles/RaisingChildrenD...
http://www.dpw.state.pa.us/Child/BehavHealthServChildren/...
http://www.ciccparenting.org/NewsLetters/Defiant_Children...
http://www.schwablearning.org/articles.aspx?r=776&WT....
Take care!
D.