Here's what rhymes with theroux.
to who you do two new through too few view due knew du u threw coup flew qu shoe zu anew dew hue lieu shew su sue tu vous chew deux flue fu lu rue slew stew zoo adieu ado bu flu hu ju jus ku loo mu nu peu pu seu shu sou thru vu woo yew yu boo chou chu coo cou doo ewe feu fue gu hew ru shou shrew thu tue vou vue wou wu goo moo pooh poo shoo gnu roux slue thew whew phew true blue drew grew que crew pursue blew q screw avenue canoe clue cue glue queue undue accrue cu subdue taboo undo brew overdue pew skew tattoo eschew mieux shampoo sprue tzu vnto clew mew overdo strew halloo spew valuer zebu kazoo overshoe wazoo achoo into review revenue hitherto overview residue bamboo renew ensue untrue jusqu overthrew piu beaucoup outdo revue sinew askew redo fondue foreknew overflew overdrew overgrew booboo regrew atishoo withdrew debut retinue kangaroo imbue outgrew cockatoo honeydew bugaboo endue indue marabou peekaboo bestrew buckaroo muumuu prevue superglue interview caribou construe ballyhoo hullabaloo rendezvous barbecue misconstrue barbeque