OSMC, RPi2 - continuous out-of-memory problem

Return code 137 means that Kodi was terminated with signal 9, (137-128=9) which is SIGKILL. So all that is telling you is that the out of memory killer killed Kodi with SIGKILL.

What would be useful is if you monitor free memory via SSH using ‘top’ to see what is actually using the memory - run top, then press ‘c’ to show full process names and then M (capital M) to sort by memory use.

BTW please use the paste-log command to upload logs, don’t paste large logs directly into your post.