Okay, we have something shameful to admit: we don't speak Ancient Chinese. Well, we guess it's not too shameful since most modern Chinese speakers don't either—just as the vast majority of modern English speakers barely recognize the Middle English of the Canterbury Tales and have zero idea of what the Old English in Beowulf is saying.
So since we can't crack the code of the Ancient Chinese characters in which the Tao Te Ching was originally written, we'd have a tough time taking you through the sonic devices it uses. Different English translators do different things and, of course, none of it sounds a lick like Ancient Chinese. We can tell you, however, that the experts say that chunks of the original TTC do rhyme, and that the whole thing has a real flow to it.
Also, we're told that the original uses a lot of repetition, which English translations can give us a little bit of a feel for. Take the famous first lines, for example:
The Tao that can be spoken is not the eternal Tao
The name that can be named is not the eternal name
The nameless is the origin of Heaven and Earth
The named is the mother of myriad things (1.1-4)
"Tao" is repeated a couple times and "name" pops up a whole bunch in various forms. So not only are these concepts repeated, but the sounds they make are also repeated. The way we figure it, this repetition of sound makes the words flow together and helps gets across the feel of the ever-flowing Tao.