Most of the email generated from the server appears to be from the user "mailnull", and it's sending out a lot of emails. Who is this user?
The user mailnull is utilized by the Exim service, this is quickly verified by reviewing the process Exim is operating under in the ps command:
# ps -uU mailnull | head -2
USER PID %CPU %MEM VSZ RSS TTY STAT START TIME COMMAND
mailnull 341 0.0 0.0 83648 5576 ? S 10:06 0:00 /usr/sbin/exim -ps -bd -q15m -oP /var/spool/exim/exim-daemon.pid