"Is any sick among you? Let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord."
When did the use of consecrated olive oil in priesthood blessings originate, and what part does the oil play in the blessing?
"Why is oil used in administering to the sick? First and foremost, of course, we use olive oil because the Lord has commanded us to do so. The scriptures give us some clues as to why the Lord has so directed us."
On one occasion, Jesus encountered a man who had been blind from birth. The Savior anointed the man’s eyes with clay and then instructed him to go and wash in the pool of Siloam. (See John 9:6–7.) Perhaps the Lord wanted the blind man to be anointed and washed in order for him to be physically involved in the healing process. Likewise, baptism by immersion, the sacramental bread and water, and the laying on of hands and anointing with oil all personally involve the faithful participant in the holy ordinance."
So it is with administration to the sick. We apply hands and oil, the physical touch and the tangible substance, but the hands and the oil do not heal. It is faith in Jesus Christ and the power of the priesthood that heals."
“There have been cases, sad to relate, where elders of the Church, through lack of understanding, have refused to administer to the sick under conditions where oil could not be had. It is the privilege and duty of the elders to bless the sick by the laying on of hands. If they have pure olive oil which has been consecrated for this purpose, one of them should use it in anointing the sick, and then they should by the laying on of hands seal the anointing. If no oil is to be had, then they should administer by the laying on of hands in the power of the priesthood and in the prayer of faith, that the blessing sought may come through the power of the Spirit of the Lord. This is in accordance with the divine plan inaugurated in the beginning.”
~Doctrines of Salvation, comp. Bruce R. McConkie, 3 vols., Salt Lake City: Bookcraft, 1954–56, 3:183.~
Anointing of the Sick
"An important part of anointing the sick, sealing the anointing, and pronouncing a blessing of healing is the faith of the recipient. Being healed through an administration of the priesthood is a fruit of faith in the Lord Jesus Christ and His ability to heal.
To the father who brought his son to Jesus to be healed, Jesus said, “If thou canst believe, all things are possible to him that believeth.” The father, knowing he believed, but perhaps worried that his faith was not enough, answered, “Lord, I believe; help thou mine unbelief” (Mark 9:23–24). The son was healed.
Although members of The Church of Jesus Christ are usually those who ask for blessings, anyone who wants a blessing, including an anointing, can have one. As James said, “Is any sick among you? Let him call for the elders of the church” (James 5:14, emphasis added). Melchizedek Priesthood holders are willing to administer to all people."
If you wanted to be really fancy and got loot to spare you can always get an oil vial engraved with your Priesthood Line of Authority HERE. I'd like one myself but I don't mind being poor and having to use glass and aluminium, as shown at the top.