The Kidou-shuu (鬼道衆) or Demoniacal Horde in the English dub, is a cult whose members use Gehou (外法), or the Dark Arts. Tendou Kodzunu is their leader as he is the embodiment of their black magic, the most powerful.
In the anime, there is only reference to the five demonic leaders and Kodzunu, and that they are all of the current existing Kidou-shuu. The five leaders appear to be spirits serving Kodzunu, and are eventually reincarnated into the physical world as demons.
The Kidou-shuu make their first appearance in the self-titled episode seven of the first season.
The five leaders of the Dark Arts are based on the elements, and are symbolized by the single horn growing from an eye socket. They are:
Enkaku 炎角（えんかく） Fire Horn. His powers are based on manipulating flames, and his appearance is said to be semi-dragon.
Gankaku 岩角（がんかく） Earth Horn. Originally, he is one of the first Kidou-shuu to encounter the protagonists. His attacks are brute strength, enough to break rocks, and his appearance is half-ox.
Fuukaku 風角（ふうかく） Wind Horn. He has the deepest devoted allegiance to Tendou Kodzunu, and his attacks are wind-based, likened to Kamaitachi (folklore monsters that slash using whirlwinds).
Raikaku 雷角（らいかく） Literally Thunder Horn, but more commonly called Lightning Horn. Master of "thunder ninjutsu" and all of his attacks are lightning center; he also fights using a spear. His strengths are a lot like Raito Umon's powers. His appearance is half-beast.
Suikaku 水角（すいかく） Water Horn. The lone woman in the Kidou-shuu, her powers are manipulating water to attack, plus she fights with a short sword. She can change people into water monsters, as seen in the videogame when she turns fellow Kidou-shuu member Ryou Mizuki (not in the anime) into a demon. Her appearance is mostly that of a spider, which is not shown in the anime. Suikaku is the only member to get an extended story for the DS re-release edition of the videogame.
In the anime, the Kidou-shuu is given a backstory that is shrouded in misconceptions and retellings. Only Munetaka Yagyuu, Tendou Kodzunu, and Ryuuzan Arai know the full, true history.
The Kidou-shuu and Kodzunu Clan were accused of forming an army against the Tokugawa shogunate during the Bakumatsu (late Edo period) and resorting to the Dark Arts to transform their numbers into ferocious demons. Calling upon the black magic left them without allies, and they were defeated. Since their fall, the Kidou-shuu was thought to be disolved, and the Kodzunu heirs were hunted to near exitinction, the remaining hiding behind false names.Apparently, the clan was not as malicious as many had thought over the years, and instead their army was formed when the shogunate kidnapped one of their own - a young woman with the Bosatsu-gan (Bodhisattva Eye). So in the end, it was the Kodzunu's Kidou-shuu victimized for wanting to protect the girl.
Because of this tragic history, repeated in his own lifetime, Tendou Kodzunu seeks to resurrect the spirit of Kishuu Kodzunu, the Master of the Dark Arts who was killed on the battlefield during the Bakumatsu.
This backstory is untrue in the original versions. The Kidou-shuu is formed to indeed fight the shogunate.
In the manga and game, the Kidou-shuu is a secretive cult and has a mass following. Its members wear ninja-like gear and hide their faces behind masks made to resemble oni (ogres or demons). While the Kidou-shuu five leaders and Kodzunu do transform many followers into monsters (as in the anime), most of the people are already loyal members and practice the Dark Arts of their own will. The Horns themselves in the videogame are still human, powerful mages, until Tendou Kodzunu transforms them into demons as a display of his own strength. However, the Horned leaders are not fully recognized in the manga adaption, instead only featuring demons with antlers and horns.