The song that Eric sings while in Ops is "I Am The Very Model..." from "The Pirates of Penzance" by Gilbert and Sullivan.
The tune that Eric hums earlier (around 13mins) is also from The Pirates of Penzance. It's the refrain, "Come friends who plough the sea...", from the chorus "With cat-like tread, upon our prey we steal". There was a production of Pirates in Los Angeles in 2007, with Rex Smith as the Pirate King - perhaps Eric had been to see that.