Overdoing rhymes with:
dewing, doing, outdoing, redoing, subduing, undoing, accruing, blueing, bluing, booing, brewing, canoeing, chewing, cooing, cuing, debuting, dewing, doing, eschewing, ewing, hewing, lewing, misconstruing, nonaccruing, outdoing, pursuing, queuing, redoing, renewing, reviewing, screwing, skewing, spewing, stewing, subduing, suing, tattooing, undoing, viewing, wooing
Overdoing sounds like:
operating, operation's, operations, operations', overeating, overheating, overrating, overriding, overtones, overwriting