Even though the product name ‘ODROID’ is a portmanteau of ‘open’ + ‘Android’, the hardware isn't actually fully open source because some parts of the design are still retained proprietary by the Hardkernel company or by ARM itself, such as the graphics drivers. As a home media center this line of boards offers a very cheap HTPC clients that as a media player in many cases works better than similar devices like the Raspberry Pi series.
The best option for Kodi is to use the LibreELEC distribution made by user wrxtasy at the Hardkernel Forums. However the official Ubuntu image from HardKernel also includes a modified version of Kodi (though often outdated and can not be easily updated).
The well known XBMC Media Center has been renamed to Kodi with the 14.0 Helix release and following upstream’s decision the xbmc packages are renamed to kodi as well. Debian ships a slightly changed version of XBMC using the “XBMC from Debian” name and following that tradition ladies and gentlemen let me introduce you “Kodi from Debian”:
Open Embedded Linux Entertainment Center (OpenELEC) is a small Linux distribution built from scratch as a platform to turn your computer into a Kodi (previously XBMC) media center. OpenELEC is designed to make your system boot fast, and the install is so easy that anyone can turn a blank PC into a media machine in less than 15 minutes.
OpenELEC is an embedded operating system built specifically to run Kodi (formerly known as XBMC), the open source entertainment media hub. The idea behind OpenELEC is to allow people to use their Home Theatre PC (HTPC) like any other device you might have attached to your TV, like a DVD player or Sky box. Instead of having to manage a full operating system, configure it and install the packages required to turn it into a hybrid media center, OpenELEC is designed to be simple to install, manage and use, making it more like running a set-top box than a full-blown computer.