I'm using MS Office 2016 One note on windows 10.
On my PC, when I put box-drawing characters as like this : ┴┻┷┸┸┵┶┹┺┐┐┘├┬┬┤┴┼┣┳┼ on OneNote 2016 on Windows 10 those will be shown as ⍰⍰⍰⍰⍰⍰⍰⍰⍰┐┐┘⍰⍰⍰⍰⍰⍰⍰⍰⍰. Some of these seem like a missing glyph, but some of those are displayed properly, I've changed fonts but I still get the same result. I've also tested it on different office 2016's products but this only occurred on OneNote 2016.
Any possible solutions?
The reason why this doesn't work has nothing to do with the fonts as you've found. OneNote simply doesn't support unicode as has been reported here and the same issue, but more generally can be found also in this article.
As the following excerpt about the Windows 10 Edition(but should mostly apply to other versions as well) explains, a font fallback system is used for most applications to help them display characters not in a font.
All Windows 10 editions include fonts that provide broad language support, and the Windows platform includes font fallback mechanisms designed to ensure that text in any language always displays with legible glyphs rather than boxes. But some apps may take direct dependencies on particular fonts for displaying certain Unicode characters and do not utilize the font fallback mechanisms provided by Windows 10 systems"
(emphasis mine)
However this explanation neglects how Windows actually uses fonts and why a font fallback is necessary. The way that most applications in Windows handle text is:
Find the font it wants. Depending on the application it might look for a font file that comes bundled with it, or looks for the font in the Windows Font Directory if it's a commonly used font.
Displays the characters the chosen font supports. This contains characters to display, but not all of them, as there are 137,174 Unicode Characters and designing a single font for all of them is impossible because a font file simply can't contain that many characters.
However there are font families that are attempting to do this such as Google Noto.
Uses "font fallbacks" if the application uses them to display unsupported unicode. Windows knows that no font file can support all Unicode Characters so it has a system that inserts fonts for different languages and sections of Unicode.
Older applications such as OneNote may support sections or languages of this in a more manual way, but ultimately doesn't use the font fallback system, and so doesn't support all Unicode Characters. Which leads to the next step
Windows displays the "not defined" glyph this usually has the appearance of a rectangular box as you've seen, this can be "overridden" in a font, and depending on the OS or even application may appear as a black question mark.
The reason why OneNote has so many of these font issues is because it is a legacy program. In fact, the version you have stated you use, OneNote 2016 is being Sunsetted and as such will not be getting any more updates, so there is likely no fix for this beyond using a different application.
Disclaimer: I am not an expert nor will I pretend to be, I hope that this represents an accurate explanation, but cannot guarantee it. I may turn this into a community wiki later, but I plan to research this topic more to verify it.