You will need to get the top output while the issues are happening.
Add a script like this to /usr/bin/top-watch.sh:
top -b -n 1 >> $LOGFILE
Make it executable, then add a crontab entry to run it every 5 minutes (for example):
0-55/5 * * * * /bin/sh /usr/bin/top-watch.sh
Once this is done you can look through the logs of the times when the load was high and only paste the top output from those times.
If there isn't enough information after this output, you may need to get a copy of /proc/*/status to check the process states/memory usage, etc... with vmstat output.