They appear to be supernatural tools summoned to perform a task without any personal motivation or animus.
Oni appear again in Season 5 and Season 6 as visions. One is created by the Skinwalkers to test Kira and the Anuk-Ite takes the form of an Oni in an attempt to frighten Scott. (Codominance, The Wolves of War)
All of our background and history about the Oni comes from Silverfinger.
The old Yakuza's description is more poetic than probative.
In both instances seen in Teen Wolf, Chris Argent as a teen and the current story line, Oni seek a "dark Kitsune" also described as a "dark spirit" that has possessed someone.
Silverfinger claims they are unstoppable and that "no man-made" weapon can stop them.
He describes them as a "force of nature" comparable to a tsunami. He says they are not to be fought but simply endured until they finish their work.
Like the weather, the Oni are neither good nor evil. They are simply given a task and will let nothing stop them in the pursuit of that task. They kill anyone who opposes them.
The Oni seen most recently on the show were summoned and controlled by the breaking of special knives which are apparently the physical manifestation of Kitsune Noshiko Yukimura's tails. The age of the "tail" determined the "power" of the Oni summoned.
They can phase through solid matter, are skilled in martial arts combat, and fight with Ninjatō or straight swords.
Oni cannot operate from sunrise to sundown.
While "man-made" weapons are not supposed to harm or kill the Oni, a silver bullet forged by Chris Argent and silver arrowheads forged by Allison Argent were able to penetrate the outer garments and release the spirit within. (Insatiable, The Divine Move)
The Nogitsune was also able to stop the creature by snatching a firefly from within an Oni body. (Silverfinger)
If the individual is not possessed, the Oni leave a mark on their neck (behind the left ear).
It looks like a backwards 5 is actually "己" which is the Kanji for "self" to indicate the subject is not possessed.
Characters marked on the show:
Stiles was also marked but not until after the Nogitsune split off from his body.
The Oni appear to be genuinely "morally neutral" in that they are not motivated by concepts of good or evil.
The summoner gives them a task, in this case "find and destroy the nogitsune," and the Oni pursue the task until completion or until they are destroyed.
While we might describe that goal as "good", their methods are not. They do not hesitate to cut down anyone who appears to block them from their task.
When a malevolent force takes control of them (the Nogitsune using Noshiko Yukimura's last, and oldest, tail) they are equally aggressive in protecting that which they formerly hunted (See Insatiable).