One of my favorite Elrond headcanons is the idea that he starts out looking very much human and elvish. He has ears too pointed to be a man's, but not nearly long enough to be an elf's, his father's (grandfather's, really) blue eyes and brown hair that shines like an elf's, but gets tangled far too often.
Sure, some weird things happen around Elrond as a child– the birds that seems to follow him, the way some injuries mysteriously resolve in his prescense, the unusual flowers that bloom outside his windows– but really, it's easy to see those as distant remnants of an ainuric power that Elrond clearly didn't inherit. When he comes to Gil-Galad's camp, it's much easier for them to see Tuor or Beren in him than it is to think he's descended from Melian.
But then time passes. The changes are slow enough– happening over decades or centuries– that no one really notices at first. Elrond's hair darkens until it is as black as the night sky– as black as Luthien's was. His eyes leach color until they are gray– not Noldor gray, mind, but a strange, starry gray that some of the Iathrim whisper about. His voice changes, almost seems to take on an echo of itself, sometimes.
The strange things that happen around him only get stranger– the trees bend to shelter him, during storms, and sometimes when he sings, the birds sing with him. Elrond got a cat, right at the start of the Second Age– a gift from Gil-Galad. Somehow, it never seems to grow old or die. The parts of Lindon Elrond most often visits always seem to be in full bloom, no matter what season it is. His healing abilities surpass what is to be expected of a man– an elf– eventually, of what seems possible at all.
At the end of the First Age, it would've been hard to believe Elrond had more than a trickle of ainur blood in him. By the beginning of the Third Age, many have started to whisper about Rivendell– a new Doriath, ruled by a Maiarin lord with all Melian's grace, and her eccentricities.
Elrond doesn't realize just how much he's changed until the day, late in the Third Age, when he finds Maglor wandering on the shoreline. Nothing he says will convince Maglor that he isn't Luthien's spirit, returned from death to haunt him.