I’ve read The Hellbound Heart, the novel the first film is based on, and read nearly every issue of the Hellraiser comic (Plus the annual Book Of The Damned, and the summer specials, and the Christmas special), The horrible Harrowers comic, as well as the Pinhead miniseries.
What 5 and 6? IIRC
Hellraiser
Hellraiser II- Hellbound
At the end of this Pinhead, or at least parts of him, is incorporated into a spiked ornamental column.
Hellraiser III- Hell On Earth
At the beginning, we see the small, stone column covered in some kind of liquid and transformed into the pillar of souls statue seen in the rest of the film. Eliott Spenser, the soldier who became Pinhead, contacts a woman through her dreams and reveals that he and Pinhead have become seperated. Pinhead is no longer bound by the laws of Hell or any vestige of conscience. They are rejoined and sent to hell at the end of the film.
Hellraiser IV- Bloodlines
Starts with the tale of how LeMerchand made the first Lament Configuration and traces his descendants through the centuries.
Note that the Cenobites’ popularity is shown through the fact the credits of the first film give descriptions of them rather than names. The credits of the second film give all but the female cenobite names. IMHO Pinhead became popular partly due to the fetish part of his nature- body piercing, leather, sadomasochism, and partly due to his speeches. Jason, Leatherface, and Michael Meyers only grunted occasionally. Freddy and Chuckie spoke mostly in cliches and bad puns. Pinhead spoke with an odd mix of cold detachment and hot passion, and in marvellous sermons.
The comics, especially (obviously) the Pinhead miniseries, do explain how Pinhead became so powerful. Several articles on the 3 suggest that originally this was also to be shown in that film, but was dropped. Where Leviathan came from or how, is unknown. But, it is a being of perfect order. The abundance of chaotic life on a primal earth, broke the barrier between our dimensions. In order to defend itself, Leviathan made a servant of certain ape. He taught others how to make fire, build tools, and how to become strong by imposing order on the world. Somehow, this protoCenobite died.Leviathan recaptured the part of itself it had given the ape and put it into a new vessel. Other cenobites are simply humans who have been remade. Their forms and abilities are based on who they were in their lives as humans. Pinhead is more than this. Part of him is Spenser remade. But he is also the most recent vessel of the fragment of Leviathan which was placed in the first Cenobite. This is why the other Cenobites follow him and why he can command the hooked chains of Hell with his thoughts. He is the favored son of the Lord Of The Labyrinth.
Before Pinhead were- A protohuman Cenobite with small bones piercing his scalp, Bel Alla a Sumerian warrior, Xipe Totec a Mayan warrior priest, A Cardinal whose name escapes me at the moment, an unnamed Cenobite with large gears piercing his skull, and Arrowhead a Cherokee whose face was pierced with (you guessed it) arrowheads. Presumably after Pinhead, Leviathan will place the fragment in a new human host.
Some Cenobites worship Pinhead as a god in his own right. He feels that this is blasphemy and “There can be only one god in Hell.”. He prefers that other Cenobites call him master, or other titles. There are rumors that he will destroy any Cenobite who calls him Pinhead.