A sh!tbox car is one that is worn out car that is falling apart, litterally leaving a trail of parts down the highway.

The sonic part comes from the fact that this car is equipped with a fart cannon muffler. the term sonic sh!tbox usually implies that the car is eurotrash.
tom: gee i gotta work on that junk car of mine, dang 500 dollar sway bar bushing is shot
andy: 500 bucks for a sway bar bu...HEY, you have a fart cannon on that Saab?
tom:oh yea, alll these expensive parts means i have no money for a real muffler
andy:yep, that's official, Sonic Sh!tbox
by tghnjolk,mdfe April 03, 2013

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