Like the OP, I had some issues with installing Java 8 (required by FileBot) on a recent OSMC (2017-02).
As implicitly concluded above, the default-jre-headless package currently installs Java 7. So Jessie backports as suggested by sam_nazarko is a good solution. I’ll just add some detail.
To enable Jessie backports and make its contents available, do something like:
echo deb http://ftp.debian.org/debian jessie-backports main | sudo tee --append /etc/apt/sources.list
sudo apt-get update
To install the JRE package, there’s a special quirk:
sudo apt-get -t jessie-backports install openjdk-8-jre-headless
If “-t jessie-backports” is not included, it complains of a dependency problem and won’t install.
After this I can verify Java 8 is installed.
$ java -version
openjdk version "1.8.0_121"
OpenJDK Runtime Environment (build 1.8.0_121-8u121-b13-1~bpo8+1-b13)
OpenJDK Zero VM (build 25.121-b13, interpreted mode)
(And now FileBot works too.)