Start with never, ever give in. When you give in once in awhile she's going to try the tantrum to see if this will be the time you give in.
What do you do when she throws a tantrum? I suggest that you need to walk away every time. Do not give her any attention when she's having a fit. It's no fun to scream when no one is paying attention. Or you can send/take her to her room and tell her she can come out when she is calm and ready to do what you asked. It will take many times of her tantruming and you ignoring her before she'll stop. If you send her to her room you will have to take her back to her room many times. It takes twice or even three times as long to change a behavior as it did to form it.
Then give her positive attention every change you get. Kids want their parent's approval. She will gradually learn to work towards getting that hug, that kind word if you're consistent in giving her approval.
And I suggest you pick a couple of things to focus on because it sounds like she's fighting everything. Perhaps start with picking up. Tell her, when you're both calm that she'll have 20 minutes to pick up her toys and if she doesn't you're going to put them away and she'll have to earn them back. Start out helping her to pick up the toys. Make a game and have fun picking up toys. After a couple of successful times doing this tell her you know she can pick them up by herself. Then leave the room. Come back in 20 minutes and if toys are still out, pick them up and put them away. Do not respond to her tantrum. Leave the room with the toys.
When I say do not respond, I mean literally do not talk to her. Do not make a face. Have no reaction whatsoever.
I would let the homework go for now. Let her suffer the natural consequences she'll get at school when she doesn't turn it in. Talk with the teacher and tell her you're having difficulty getting her to mind and that you're starting with other issues. Nearly all parents, even those with well behaved children have some issues with getting homework done. Start being consistent with immediate consequences with simpler tasks.
Never let her see you "sweat." Never argue or try to convince her to do something. If you find yourself needing to yell remove yourself from the room before you yell. I suggest that by picking a couple of behaviors on which to focus and letting others go you'll be less stressed. You cannot change everything at once.
Think of logical consequences for misbehavior. She doesn't get dressed take her in her pjs. No fight there. Give her a choice of two movies, both of which you approve. She throws a tantrum, no movie. That's part of the ignoring. When she interrupts conversation, completely ignore her. Stop talking until she stops talking. You can give her the "eye" but it's also OK to not even look at her.
Whatever you decide to do for consequences you have to always follow thru. You have to be totally consistent with using the same technique every time. Stop trying out various things. Decide what you're going to do and stick with it. Never give in. This will be hard and a lot of work but you can do it.
I also suggest that you read Love and Logic by Foster Cline. And, tho I've not used it, I've heard a lot of good words about 1-2-3 Magic and Back to Basics by Janet Campbell.