Squick: Possibly a contraction of "squeamish" and "Ick!" A negative emotional response, more specifically a disturbed or disgusted one.
"Squicky" and "squicked" are also common forms, with The Other Tropes Wiki having apparently invented the form "squicktastic".
Not to be confused with Squee, the very opposite. We hope.
Things that make the audience throw up often make the characters throw up as well. We have a whole pile of Disgust Tropes for in-universe squick.
The term originated on UseNet during the 1990s, although just where and when depends on who you ask. The Urban Dictionary claims it was coined in 1994 in the alt.tasteless newsgroup. Wiktionary and several other sources all point to alt.sex.bondage and hedge their bets by saying "before 1995"; Wiktionary also notes that alt.tasteless popularized it.