The spells used by Aleister and Mathers to build up their bodies at the start of their battle derive from two sets of initials, both referring to the Son of God.
Aleister makes use of the pentagrammaton, Y-H-Sh-V-H, derived from the tetragrammaton, Y-H-V-H.
Mathers makes use of INRI, short for Iēsus Nazarēnus, Rēx Iūdaeōrum (Latin for Jesus of Nazareth, King of the Jews), and said to have been carved onto the cross used in the Crucifixion.
The staff that becomes a palm tree, wielded by Aleister, is derived from the tale of St. Christopher, a large and strong Caananite initially called Reprobus who decided to serve "the greatest king there was". He initially served under the king of Canaan but after learning that the king feared the devil, he looked for the devil and came across a group of marauders, one of whom claimed to be the devil and whom he decided to serve. He later saw his master avoid a wayside cross and learned that the devil feared Christ, and left to find Christ. Following instruction and advice from a Christian hermit, Christopher served by assisting people in crossing a dangerous river. After a while, a child asked him to help him across the river, which swelled during the crossing. The child felt immensely heavy and Christopher barely managed to carry him across. Once they were across, the child revealed himself to be Christ and then disappeared. Christopher would eventually be martyred in Lycia.
The spell which Aleister used to banish Uriel and drag the other archangels with it is derived from the fact that Uriel's name isn't featured in the Bible and Pope Zachary's synod of 745 AD to clarify the church's teachings on angels and to discourage angel worship, in which many angels' names were struck from the list eligible for veneration, including Uriel.
The spell which Mathers uses to turn the hellfire from Aleister's spell back against him in the form of a pig is based on the exorcism of the Gerasene demoniac (also called the "Miracle of the (Gadarene) Swine"), a story from the gospels where Jesus Christ exorcised a legion of demons from a man and cast them into a herd of swine.