I don't know that there is anything in Buddhist teachings per se that refer to (let's call them) 'unexplained phenomena' of various religions.
And I say 'various religions' rather than 'other religions' because I want to avoid the presumption that Buddhism is by default, a religion, because there are a lot of 'unexplained phenomena' in the world. Tagging 'religion' onto it interjects a factor which may or may not really be pertinent.
Let's consider that perhaps 'unexplained phenomena' are only 'unexplained' when we do not have an answer which seems plausible. But what seems plausible is really dependent on one's attachment. Let me give you an example of what I mean:
A few years ago i was listening to a call-in radio program, where the guest's topic was the 'power of prayer' in healing the sick (this call-in show, by the way, was not on a religious station. It was on an NPR affiliate station). The guest cited a study done by a Harvard University professor, a scientifically conducted study. Patients in a hospital who had been prayed for demonstrated a higher rate of recovery than those who did not receive prayers. the guest concluded that this showed evidence of God.
I called in and ask if it was possible that the study had been contaminated. He asked what I meant. I asked him how could they be sure that there weren't invisible unicorns in the hospital giving patients magical healing rainbow kisses. The guest didn't have a whole lot to say after that.
So, my point is that while "God" and "invisible unicorns" are in fact equally possible explanations, people gravitate towards answers which, because of some sort of previous conditioning, they think are more plausible. I have yet to see 'unexplained phenomena' that wasn't somehow explained by simple science. As far as Catholic miracles are concerned, such as Virgin Mary statues crying blood or whatever, again, how do we know it isn't just some invisible unicorn playing a joke by peeing on her face to make it look like tears?
It is only because invisible unicorns are, for purely subjective reasons, not accepted as a plausible explanation (and for Vatican - hired 'scientists', God is) that various 'plausible' explanations are offered as proof.
Fortunately, 'unexplained phenomena' is not a prerequisite for practicing dharma.
there may be ghosts and devas and unicorns and rainbow bodies and all sorts of things that I have never seen. But until I see them, this is the best answer I can give. One needs to look at their attachment to the plausibility factor of various explanations for 'unexplained phenomena'
Profile Picture: "The Foaming Monk"
The Chinese characters are Fo (buddha) and Ming (bright). The image is of a student of Buddhism, who, imagining himself to be a monk, and not understanding the true meaning of the words takes the sound of the words literally. Likewise, People on web forums sometime seem to be foaming at the mouth. Original painting by P.Volker /used by permission.