To list the processes sorted by the memory usage
ps --sort -rss -eo pid,pmem,rss,vsz,comm
More information here : how-to-detect-a-memory-leak
The server is killing processes to free memory, this is what happens when all the virtual pages are allocated (swap+ram). If possible the best would be to restart the server to have all the stopped services restarted and and memory free.
More information here : Debug out-of-memory with /var/log/messages
May 8 03:53:21 bwnet kernel: [5088999.370529] Free swap = 0kB May 8 03:53:21 bwnet kernel: [5088999.370530] Total swap = 0kB
Reading your logs it seems that you have no swap. You may allocate some, that will allows you to manage the problem before it becomes critical.