Have you tried the products yet? Head and shoulders type stuff work for dandruff due to the active ingredients in it, and I believe it would work fine for oily dandruff.
Dandruff can cause either an overly dry scalp with itchy white flakes that may be waxy or greasy, or it can manifest as an oily scalp with scales.
Eat a healthy diet. You can also take vit B6 and vit A and E which are good for hair and skin. Try medicated shampoos for dandruff. There are a number of over-the-counter shampoos available that can help. The most effective ingredients -- antimicrobials -- to look for are zinc pyridinethione, selenium sulfide, sulfur and ketoconazole (also available by prescription). If your hair is colored, don't use products with selenium sulfide or sulfur.
If the symptoms persist please consult a trichologist. It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.