How can I cure greasy hair and dandruff using home remedies?

Shampoos are helpful. Dandruff (seborheic dermatitis) will usually clear with selsun blue or ketoconazole shampoo in 1-2 weeks if the case is mild. You may also find some success with salicylic acid or tar shampoos or a specific shampoo called dhs zinc. Sometimes it is more severe and will require more aggressive treatment. See your doctor or a dermatologist if the above is not helping after a couple weeks.