When Kim Jong Ill is singing about how lonely he is, it's logical to assume it's because he's a tyrant whom no one loves or likes. However, considering that he's actually an alien cockroach sent to conquer the Earth, it makes perfect sense: he's singing about there's no one like him on the planet, and thus, is completely alone.
The song "Pearl Harbor Sucked" plays before Gary returns to the team. Since he's a great actor, he would have a love song bashing a crappy romantic drama running through his head. In fact, he's the one singing it.