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