John - Spongebob.
Dave and Bro - Such thick Texan accents that nobody can understand them. I was going to do an animation about it, but couldn't find the time. I only ever animated Bro saying "schnahshehpowcwahcopfhshiypbompbwahpbacapbopbadaeboobz". (audio here)
CD - Irish. That is all.
Jack/Bec Noir - Jack from Jacksfilms. And almost incessantly making horrible dog puns.
Sollux - William Murderface MURDERFACE MURDERFACE of Dethklok.
Karkat - Screaming like a banshee all the time. Even when he's being sentimental he screams. So loudly that his voice loses all semblance of tone. Also, this is the sound he makes when he does that mouth-flapping crab thing.
Kanaya - I read "Your trolltag is grimAuxiliatrix and you Tend To Enunciate Each Word You Speak Very Clearly And Carefully" and immediately pictured her sounding everything out slowly like she's reading a book to small children, and taking upwards of a minute to finish each sentence.
Terezi - The gravelly male voice of an old Southern reverend. This comic did it.
Eridan - Mike Tyson's voice, but halfway to falsetto. Not a clue why, probably just rule of funny.
Feferi: Really really high-pitched, emotive Disney-princess-style voice, but upon getting really -EXCIT-ED she'll randomly scream certain sentence fragments and sound like Patrick Warburton. Lord knows why I thought of this.
Jane: Swedish Chef, as demonstrated here.