The Oni are a neutral force that can be summoned through mystical rituals, though the exact details of the summoning rituals are unknown and seem to vary depending on the person who is summoning them though a supernatural power source of some kind seems to be a necessity.
When Noshiko Yukimura summoned the Oni, she did so by breaking her Kitsune tails as a power source, which allowed the Oni to come to the living world through a portal in the Nemeton and materialize from a cloud swirling darkness and hundreds of fireflies; Noshiko started with her most-recently gained tails and worked her way up to the older ones, which meant that each Oni was increasingly stronger than the other.
Once the Oni has been summoned, they will single-mindedly and obediently fulfill the commands of the person or creature that summoned them; this typically involves hunting down and slaying a Nogitsune, though this is not always the case. Regardless of the reasoning behind why they were summoned, they will not stop until they have completed their mission or are killed. However, control over these summoned Oni can be taken by someone with a stronger power source, as the Nogitsune did when he used one of Noshiko's oldest tails to make her Oni loyal to him instead, this required him to be in very close quarters with the Oni, a dangerous gambit considering their single minded goal to destroy him.
A Desert Oni was summoned by the Skinwalkers through unknown means and appeared from within a cloud of dust created by a gust of wind after the sun had set in the desert of Shiprock, New Mexico. The Desert One was in fact a Projection manifested by the Skin walkers rather than a true Oni.