"Immortals" is a generic term used for several beings that have been around for centuries - perhaps since the dawn of time. Some of them appear to have powers that place them in the range of gods, or at least demigods. While others do not display powers of their own, but make references to knowing gods personally.
They are most certainly not a "faction" like other Factions in the game. Instead they are a group of individuals that unique enough that they deserve their own mention.
Their origins and powers are unknown. It could be that they all share an origination event/story. It could be that they all started out as something else and become immortals. Or, it could be that they are indeed completely unique individuals with no real relationship to each other beyond their immortality.
However, players are given clues that several of these beings know each other, or at least know of each other, and are often struggling for supremacy over each other. It seems as if they are operating in what could be called a "Secret World" above and beyond the Secret World that players are aware of.
With no fixed organization and the ability to apparently travel over the world at will, they have no fixed locations are centers of power. At least, not on this world. Although, there seems to be areas of the earth that some of them return to more often.
- Aten - The The Seven Sentinels say he is not a god. His worshipers and the Pharaohs of Egypt would say otherwise. Exactly what his status is, is uncertain.
- Cassandra King - Very unlikely to be her real name.... She had enough knowledge and power to take the sword from Freddy Beaumont.
- Cucuvea - She mentions having lived during the Third Age as well as "fighting off Lilith's children".
- Emma Smith - Lilith and The Filth seem to want her for their own uses, and she is apparently powerful enough to fight them off. She claims her name is "Anima", and perhaps she is Anima incarnate.
- Freddy Beaumont - He boasts of having fought gods, and having been "kicked out" because they feared his ideas. There are hints that he is perhaps also known as Loki
- Khalid El Sayad - Says he is immortal. Also mentions being part of the four-and-sixty but parted ways with them because he cared too much about mortals. His brother is "a bothersome spirit that likes to put on a show" (burn bushes). Also referred to as one of the Immortals in the How Can We Be Sure? achievement.
- Lilith - She tries to kidnap Emma. She claims to be the original Lilith from the bible, along with several other goddesses. The leaders of the Templars, Illuminati, and The Dragon seem to believe her
- Moşul - Mentions having been in Transylvania since long before the fall of the Roman Empire
- Ptahmose - Sacrificed his children to trap the Aten in the pyramid. Referred to as one of the Immortals in the How Can We Be Sure? achievement
Four and Sixty
The "Four and Sixty" are mentioned a couple of times, but never explained.
- John Wolf - One of the Four and Sixty, John is stationed in Solomon Island, along with his partner, Jack Boone. 
- Khalid El Sayad - Says he was a member of the Four and Sixty, but he left them because he "cared too much about mortals" ,
- Anastasia mentions that "the three warriors were bound by oath to the Sixty-and-Four" . The three warriors being the "Owl" - Cucuvea, the "Dragon" - Vlad Dracula, and the "Eagle" - Octavian
- The Unburnt Bush - Intro Dialogue
- Black Sun, Red Sand - Tier 3 dialogue
- Mortal Sins - Tier 7 dialogue