GAIJIN = outside person = foreigner. That'd be US.
It's impolite to call a gaijin a gaijin to his or her foreign face, but it's sort of funny when the gaijin refers to her or his own foreign self as "gaijin".

PEKO-PEKO = hungry (a loaner from the British "peckish", maybe?)

Japanese has hundreds (thousands!) of words that are onomatopoetic (HEY, the spellchecker liked it!) or that indicate some sort of physical or emotional state.
Most of them follow the same pattern as PEKO-PEKO, a doubled two syllable word.

And when the gaijin is peko-peko, the gaijin is in deep trouble if the gaijin doesn't know how to order food at the restaurant.

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