Given my use of non-human characters, I've dealt with the use of "accents" in pretty much all the ways mentioned here. Anything from simply stating the "strangeness" of their vocal qualities (while writing their dialog in "plain" English), through slang (I have a character who uses surfer lingo), all the way to the language mangling done by very young children. And "pidgin" English, interspersed with alien words (I have a character whose native language has an odd syntax, so his "English" is very broken/simplistic and filled with his native terms (used only when no other word fit/translated)... heh, I even had him in an RP where I had to have him explain the meaning of one of his native words to a character who didn't understand, yet wanted to know what he'd meant. That was fun...)

So, an "accent" could be created by the use of non-English terms thrown in when no other words would do, as well as by a simple twist of syntax in "translation".