Q. 1. Can a Deacon or an extraordinary minister perform anointings either with the oil of the Sick or any other oil?
A. 1. Since ordinary (Deacons) or extraordinary ministers are not priests, under no circumstances may the non-ordained perform anointings either with the Oil of the Sick or any other oil.
On this matter, the Catholic Church teaches:
Part II, Article 9. The Apostolate to the Sick
§ 1. In this area, the non-ordained faithful can often provide valuable collaboration.  Innumerable works of charity to the sick are constantly provided by the non-ordained faithful either individually or through community apostolates. These constitute an important Christian presence to sick and suffering of the greatest importance. The non- ordained faithful particularly assist the sick by being with them in difficult moments, encouraging them to receive the Sacraments of Penance and the Anointing of the Sick, by helping them to have the disposition to make a good individual confession as well as to prepare them to receive the Anointing of the Sick. In using sacramentals, the non- ordained faithful should ensure that these are in no way regarded as sacraments whose administration is proper and exclusive to the Bishop and to the priest. Since they are not priests, in no instance may the non-ordained perform anointings either with the Oil of the Sick or any other oil.
§ 2. With regard to the administration of this sacrament, ecclesiastical legislation reiterates the theologically certain doctrine and the age old usage of the Church  which regards the priest as its only valid minister.  This norm is completely coherent with the theological mystery signified and realized by means of priestly service.
It must also be affirmed that the reservation of the ministry of Anointing to the priest is related to the connection of this sacrament to the forgiveness of sin and the worthy reception of the Holy Eucharist. No other person may act as ordinary or extraordinary minister of the sacrament since such constitutes simulation of the sacrament.