dmesg -T | grep -i 'killed process'
grep -i 'killed process' /var/log/messages
grep -i 'killed process' /var/log/systlog

dstat --top-oom
cat /proc/PID/oom_score  # выводит количество очков у процесса

[Service]
 ...
  OOMScoreAdjust=-1000
 ...