What would cause my hair, teeth and tongue to itch ?

Allergic reaction: Itching is typically due to a local irriation or a allergic reaction. The allergic reaction can be topical (on the skin) or it can be more systemic. Involving the tongue and the hair, it is more likely systemic reaction to something in your environment. Does it occur in certain situations or certain places? Pinpointing the circumstances with a doctor will find the cause and treat it appropriately.

Possible allergy: By hair and teeth i presume you mean scalp and gums. This could be an allergic reaction to a food you have recently eaten. Over the counter Benadryl (diphenhydramine) should help. Another possibility could be medications you might be taking. If this happens frequently. You should see your medical doctor for an evaluation.