You say, these CPU peaks coincide with students submitting assignments? What are their numbers like?
If so, the obvious thing to investigate is a lame file system. Could be database store or the moodledata directory.
The CPU is Xeon E5620 with 1 core? (The Munin graph confirms that.) But E5620 is 4 core 8 thread CPU. How do you explain that?
About Swap: The machine should never swap. It is there for an emergency. The machine has 2 GB RAM. It is possible that this is the problem (or one of them). Study the other Munin graphs like load average and memory usage.