Burmese folk religion
These exorcists, or "ahletan hsaya", are said to possess powers that can fend away or challenge these evil demons. These exorcists were often seen as very holy, because they had to be to combat troublesome spirits. They attempt exorcisms by giving the nat offerings. As an interesting overlap with Buddhism, exorcisms can be performed by holding the Buddha up to the possessed person, in an effort to have the Nat flee. If the exorcist cannot banish this spirit alone, they often ask for the assistance of the nat-kadaw. Sorcerers, or "weikzas" also harnessed the power of these nats through many complex rituals, to gain their own supernatural powers.
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.