Exit code 139 means that Kodi crashed with a segmentation fault - which unfortunately is just a very generic type of crash caused by an invalid memory access, typically by trying to dereference a null pointer. In other words a bug in Kodi.
Other than that there are no clues in your log what the cause might be, especially when kodi does not have debugging enabled. I would start by stopping any services like nginx that might be running a webserver to see if Kodi launches - if it does go into Kodi’s settings and change the port or disable the webserver.
If that doesn’t help you could try doing a forced reinstall of Kodi - in theory it should not be necessary but maybe you have suffered some file system corruption. For a Pi 2 it would be:
sudo apt-get install rbp2-mediacenter-osmc --reinstall
Then reboot. If that doesn’t help, try renaming your .kodi directory so a new one is created - if this helps then something is probably corrupt in your .kodi folder, whether it be one of the databases, configuration files etc, in which case you would need to find it through a process of trial and error. It is also possible to enable debug mode using advancedsettings.xml to gather more information in the Kodi log: