It's fairly easy to install your own fonts in Over, but there are a few caveats.
First of all... Before you install any font, make sure you have a license to use it on another computer/device.
Also, on Android devices, you'll need to first unlock the system fonts in FONT before you can install your own fonts for free. But once you've unlocked the system fonts, have at it!
You can deliver .otf and .ttf font files to your device by email, Dropbox or any other way that you can get a file to your device.
You must access a proper font file – .otf, .ttf, or ZIP file with .otfs and/ or .ttfs.
As an experiment, I asked someone else to send me a link to a font. On iOS, when I pressed the link, an option showed up in the upper right hand-side of the screen to "Open in Over".
If you want to install fonts from a ZIP file, just press-and-hold on the ZIP file for the same option to install.
You can also manage your installed (and other) fonts by activating the font manager.