The most common uses of these sentences happen (mostly to me) while laying in bed at night.
"Oh, that one boy, Shiggity Sean, what a dreamy man. I can't wait to stare at him later... Oh, Shiggity Sean!!!"- Mom walks into bedroom asking if you are okay, you say yes, she leaves, and you keep fantasizing about the almighty Shiggity Sean.
The term used by actually good-aimed teenagers to make fun of swagfags. Usually put into a rhyming pattern, swiggity swag can be used in many terms, and can be rhymed with anything they can possibly think of, switching the "swag" part of the term with a new word, just starting with "sw". Parodying the horrible nature of people who actually think their swag can conquer anything, this puts the term into jokes, and can be laughed upon with good manner.
"Swiggity swag, all you people are fags!"
"Swiggity sway, did you have your breakfast today?"
"Swiggity swupid, you're pretty stupid."
"Swiggity swag, do you ever feel like a plastic bag?" -Katy Perry
"Swiggity swissile, here comes the missile!" -Kim Jong Un