I just found that it is possible to install apk from a USB drive on OpenR.
With the latest version 2.1.2 there is added Files application, that can browse files on attached drive and i was suprised that it can install apps too.
So you need:
1. Firmware version 2.1.x
2. FAT32 formatted USB drive
3. Download apk file (nodpi version) from official site, github or from some miror sites
4. Copy the file to the USB and plug it
5. Open Files application and navigate to USB drive in the menu on the left. If you can't see it, try to enable/disable "show internal storage" option, it should display it along with attached USB drive
6. Select the APK file and click - it will display consideration dialog, just click to forward and that's all , the app should be displayed on the list.
PLEASE NOTE - you do all this at your own risk! Sharing this info i'm not responsible to any damage that may occur. If you aren't sure of the consequences, just don't do this!