You need to be firm and set boundaries. If she starts hitting and screaming, put her into her room until she calms down. You cannot reason with a child that is in a "tantrum".
As she has a lot of energy, you need to direct that energy to physical play so that she uses it in a constructive way.
She may be picking up bad habits from the cartoons she watches - you do not say which types that she watches and some of them are quite violet. Restrict the amount of time that she watches TV, no doubt she will scream, but do not give in to her. Instead direct her attention to something that she can occupy her mind on like making cupcakes (most kids love to do that), or play hide and seek, playing outside with you or learning something new that would be exciting for her. Children usually like to go into the swimming pool and if she does not go yet, you could start her to have swimming lessons or go with her once a week.
Young children can exhibit anger when they begin to come down with an illness. Other times it can be from lack of sleep. If she is constantly moving about, keep an eye out for any threadworms. The tell tail signs are having itching and scratching in the anus at evening time. Sometimes you may see a white thread like worm in the toilet pan with the stools, but not often. As her if she has an itching bottom. If she does have threadworms, you can purchase medication for this without a prescription from the pharmacy. Ensure that she always washes her hands after using the toilet and before eating any food.
As she is waking up multiple times a night, she is clearly pretty tired during the day and it is no wonder that she is irritable. Cut down on all sugar foods and fizzy pop (I cannot presume that you do not give her fizzy pop, because I know that some people do give this to their children). Give her a warm milky drink or a chocolate milk shake before she goes to bed. She may have a restless sleep to being hungry or thirsty. Milky drinks are supposed to be calming.
Young children are not able to communicate properly what is wrong and she may be angry because you do not know what is wrong with her to put it right. Ask her questions to try and find out what is actually bothering her.
Once you get to the bottom of what is troubling her, I am sure she will settle down.
I would have her evaluated by an OT.
Is she in preschool?