Exorcism
In Catholic practice the person performing the exorcism, known as an exorcist, is an ordained priest. The exorcist recites prayers according to the rubrics of the rite, and may make use of religious materials such as icons and sacramentals. The exorcist invokes God—specifically the Name of Jesus—as well as members of the Church Triumphant and the Archangel Michael to intervene with the exorcism. According to Catholic understanding, several weekly exorcisms over many years are sometimes required to expel a deeply entrenched demon.
The Cairn on the Headland
Odin being in Howard's interpretation a demon, his banishment at the climax of the story is an effect an exorcism, and it includes many elements of an exorcism as depicted in Christian tradition. Holding out a crucifix is commonly mentioned as an effective method of confronting a demon. According to Christian theology - specifically, Catholic theology - one need not be a clergyman in order to perform an exorcism. However, if one is not especially holy oneself, the chances of overcoming the demon are much increased if one has a holy relic connected to a venerated Saint, thus being able to draw on that Saint's holiness. In all that, O'Brien follows on the well-established rules for carrying out an exorcism - and it works.