I am sorry to hear that your girl has stopped eating, has lost a significant amount of weight and is not herself.
Her greasy coat may be just another indication that her body isn't well. Skin and coat seem to suffer the most when a dog is dealing with a systemic illness.
With such a significant weight loss, lethargy, and loss of appetite I would be concerned about internal organ disease (especially kidney disease, but liver disease is possible too) or an infection, especially in her urinary or reproductive tract (if she is not spayed a uterine infection would be a concern) as well as ketoacidotic diabetes or cancer.
Her loss of appetite can be due to increased organ waste causing gastrointestinal irritation or by products of an infection suppressing her appetite or a mass taking up abdominal space and putting pressure on her stomach and intestines such that she doesn't want to eat.
I highly recommend that she see a veterinarian for an examination, complete blood count and biochemistry profile as well as a urinalysis and maybe abdominal radiographs or an ultrasound to diagnose her condition.
Because of the duration of her symptoms, the amount of weight she has lost and her now complete lack of water and food intake I would consider this an emergency.
Please let me know if you have any further questions.