What anesthesia is normally used for wisdom teeth removal?

Varies. Depends on the severity of the wisdom tooth impaction. I often remove wisdom teeth in my clinic with nitrous oxide and the local anesthetic articaine. If they are partially or completely impacted, an oral surgeon may use IV sedation and local anesthetic. This is a good option because you are not conscious of the procedure but not all the way under like general anesthesia.
Light Sedation. Usually this operation can be done with local anesthesia and light sedation. Some dentists use valium , other might use a combination of medications including nitrous oxide.
Varies. A few options. 1) Local anesthesia, 2) Local anesthesia with oral sedation (pill), 3) intravenous sedation for deep sedation or general anesthesia. The only practitioner to offer all options is the oral surgeon. For best results make sure you are evaluated and treated by a board certified oral & maxillofacial surgeon.
Local anesthesia. Local anesthesia (novocaine) is sufficient to prevent pain during any dental procedure including wisdom tooth removal.