Anointing with oil is performed in various ways: 1) by elders of the Church for healing, 2) Chrismation following Baptism, 3) during other Rites of Incorporation including the acceptance of Adult Communicant Members into membership and at ordinations, and 4) as a Rite of Purification in the Catechumenate and Novitiate.
Also see Chrismation, Confession, Exorcism, Forgiveness, Restitution, Rite of Incorporation, and Rite of Purification.