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.
Hardware and performance
Apache CPU High Usage when opening tasks
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