Oily FUR

Shadow_paul, it does sound like your dog has an allergy of some sort with the itching and hair loss.  Pink skin which is most noticeable under the front legs, in the groin area, between the toes and inside the ears is usually a good sign of an allergy.  Have you given her a flea treatment recently or have you seen any fleas on your dog?  Sometimes even one flea bite can cause a dog to have an allergic reaction and to scratch a lot.  If your dog is scrathing all the time, it may be worth a trip to the vet to see if it is truly an allergy and they may be able to prescribe an antihistamine.

Sometimes dogs who have problems with thier anal glands will drag thier anal area on the ground to scratch it and thus causing hair loss.  The anal glands are small pockets (grape size when full) located on either side of the rectum that are supposed to empty when a dog has a bowel movement.  They can become impacted and cannot empty themselves and can really irritate the dog.  Usually this is fixed by having the vet or technician express the glands and empty them.

Some times poor coat condition (like oily fur and hair loss) can be a symptom or a medical problem.  Aging dogs can develop medical conditions and if caught early can be treated and help extend the life of the dog. Regular vet visits and a blood work panel can help detect any early signs of disease.