Odetics rhymes with:
aesthetics, agrigenetics, anesthetics, asthmatics, athletics, bionetics, cadnetix, cognetics, cosmetics, diabetics, dianetics, diuretics, esthetics, genetics, helionetics, intermagnetics, kinetics, magnetics, metics, pharmakinetics, phonetics, prosthetics, synthetics
Odetics sounds like:
oates, oaths, oatis, oats, odaiko, oddities, odds, odes, odessa, odious, odysseus, odyssey, odyssey's, otis, otsego, otsuka, ottawa's, ottaway's, otto's, otts, out's, outage, outages, outdoes, outgo, outguess, outguesses, outhouse, outhouses, outs, outsize, outtake, outtakes, outweigh, outweighs, outwits, owades