Twang can be used in many forms, not just a silly, cartoon word, but also as a word for describing certain sounds. Guitars are plucked and make a "twang". It can be used in describing anything to do with elastic bands - when stretched and released, they make quite a distinct twang.
This is very much a casual word, however. It is not used in formal public speeches and such like, but is used in casual aquaintances, and usually is a cartoony word.
A "twang" can also be used to describe a mild accent - for example somebody from Yorkshire who has lived outside the county for many years, and whose speech has softened, could be described as having a Yorkshire twang.