Regarding Christianity in Japan, one useful bit of previous experience is the history of Christian missionaries in the 16th-17th centuries. Francis Xavier, founder of the Society of Jesus (the Jesuits) was one of them! They encountered particular issues with how best to introduce Japanese people to Christian belief, and one of the biggest problems they faced was the tendency to syncretism - the instinctive attempt to meld Christian beliefs into existing Buddhist and Shinto practice. In 1598, the confessional text Salvator Mundi / Sarobatōru Munji challenged Kirishitan (Japanese Christian) believers by asking:
Have you worshipped kami and hotoke since you became Kirishitan? If you have, how many times?
Have you worried about the punishment of kami and hotoke? Also, have you thought that they could give human beings punishment or providence?
Have you, according to pagan practices, performed the worshipping of the sun and the moon (tsuki machi hi machi), or called for a miko and an onmyōji for prayer ritual (kitō) and incantation?
Have you participated in pagan events even if you have remained Kirishitan inwardly?
Have you performed fortune-telling for yourself or made others do it? 1
I believe that the oni may be regarded essentially as a special kind of kami 2, at least for our purposes here. These early missionaries certainly saw regard for the kami as problematic, and tried to stop people from worrying about such issues as how to placate them through worship or offerings.
A belief in oni or kami, along the lines of traditional Shinto practice, is not compatible with the Christian world-view, since Christianity has different opinions about the nature and origin of spiritual beings. While Christianity does include a concept of "demon", these are not the same as Shinto "demons"; it's not reasonable to drop oni into the context of normal Christian belief. That is, it doesn't make sense to combine orthodox Christianity with a belief in oni, as oni are traditionally understood in Japanese culture. Indeed, the history of Christianity in Japan shows some problems with this approach. During the suppression of the religion, one form of "underground" Christianity transmuted into a blend of ancestor-worship/Shinto/Buddhism, with a few Christian-looking elements, but without any real connection to the core of the faith. (See this answer by AffableGeek on the Kakure Kirishitan.)
1. From Christianity in Early Modern Japan: Kirishitan Belief and Practice, Ikuo Higashibaba (BRILL, 2001), p 36-37
2. Encyclopedia of Shinto (trans. of Shinto jiten, Kobundo, 1994) under oni, senses 1 and 3, sees oni as a subcategory of kami