Anointing the sick
Whether the anointing is a sacrament of healing, a prayer, or a sign, and what the elders' role is.
James 5:14-16
14Is any among you sick? Let him call for the elders of the assembly, and let them pray over him, anointing him with oil in the name of the Lord,
15and the prayer of faith will heal him who is sick, and the Lord will raise him up. If he has committed sins, he will be forgiven.
16Confess your offenses to one another, and pray for one another, that you may be healed. The insistent prayer of a righteous person is powerfully effective.
What each tradition says
Rabbinic / Midrashic
The Jewish Encyclopedia notes that anointing was used as a remedy for skin diseases. At the same time, incantations were used, with the person anointing the head with oil also pronouncing an incantation over the sore spots. It says this practice was exactly as stated in James 5:14 and Mark 6:13.
The Jewish Encyclopedia (1905), Anointing (Jewish Encyclopedia, 1901-1906) — 'Anointing as a remedy' — the oil with incantation over the sore spots
Patristic
No sourced position found. Checked the ANF volumes fetched (ANF 1, 3, 5, 7 — including the Apostolic Constitutions' oil prayers and Book VIII, none of which cite James 5) and the NPNF volumes on hand (Chrysostom on Matthew/Acts/Romans/Corinthians/John/Hebrews; Augustine on the Psalms; Cyril of Jerusalem; the Seven Ecumenical Councils) for a public-domain patristic exposition of James 5:14-15 ('Is any sick among you... anointing him with oil'): none found. The later PD-in-Latin commentary tradition (Bede, the Glossa Ordinaria) exists in English only in modern copyrighted translations, and pravoslavieto/CCEL carry no patristic comment on the verse.
Catholic
Trent states that the proper ministers of this sacrament are the presbyters of the Church: not elders by age or the foremost in dignity among the people, but bishops or priests rightly ordained by bishops. It declares that this unction is for the sick, especially those in danger of death, and is called the sacrament of the departing.
The Council of Trent (1551), The Canons and Decrees of the Sacred and Œcumenical Council of Trent, Session XIV (trans. J. Waterworth, 1848) — Session XIV, Doctrine on the Sacrament of Extreme Unction
Orthodox
Philaret of Moscow teaches that Unction with Oil is a Sacrament. In it, while the body is anointed with oil, God’s grace is invoked on the sick to heal them of spiritual and bodily infirmities.
Philaret of Moscow, The Longer Catechism of the Orthodox, Catholic, Eastern Church (trans. R. W. Blackmore), served at pravoslavieto.com — On Unction with Oil, Q. 364-365
Reformed / Protestant
Calvin holds that James 5:14 is wickedly and ignorantly perverted when extreme unction is established by it as a sacrament to be perpetually observed in the Church. He allows that Christ’s disciples used it as a sacrament, not merely as medicine, but since the reality of this sign continued only for a time, the symbol also had to be only for a time.
John Calvin, Commentaries on the Catholic Epistles (trans. John Owen; Calvin Translation Society) — Commentary on James 5:14 ('Is any sick among you')
Evangelical
Wesley holds that anointing with oil was a conspicuous gift Christ gave the apostles, remaining after other miraculous gifts were withdrawn and designed to remain always. James directs the elders, the most if not only gifted men, to administer it; it was the church’s whole physic until lost through unbelief. The Romanist extreme unction differs entirely.
John Wesley, Explanatory Notes upon the New Testament — Notes on James 5:14 ('Having anointed him with oil')