Outdo rhymes with:
adieu, ado, badu, chengdu, deux, dew, do, doo, douwe, du, due, katmandu, ledoux, long-overdue, overdo, overdue, pas-de-deux, perdue, purdue, redo, seydoux, subdue, undo, undue, urdu, yabbadabbadoo
Outdo sounds like:
o'day, o'dea, o'dowd, oad, oat, oath, oathout, oda, oday, odd, oddi, oddity, oddy, ode, odea, oded, odette, odowd, ot, ota, otey, otha, ott, ottawa, ottaway, otte, otto, out, outdate, outdated, outdid, outed, outta, outwit, outwitted, owada, owed