Oliver awarded Madrid a last-minute penalty at the Bernabeu after Medhi Benatia fouled Lucas Vasquez, and was met by fierce opposition from Juventus' players, most notably captain Gianluigi Buffon, who was sent off for his reaction.
Cristiano Ronaldo scored the penalty to put Los Blancos through to the semi finals, having previously trailed Juventus 3-0 on the night with the tie heading towards extra time at 3-3 on aggregate.
BBC Sport report that Oliver's wife Lucy, a Women's Super League referee who also officiates non-league men's fixtures, had her mobile phone number posted on social media after the game, leading to abusive messages.
Police are looking into reports of people shouting through the letterbox of their house and banging on the front door. The mobile phone number has since been deactivated, but Lucy Oliver's social media account has still been targeted by some fans.
Elite referee's body, the PGMOL, said it was supporting the Olivers, condemning the abuse Lucy has been subjected to.
Mario Mandzukic had given Juventus the lead in Madrid on Wednesday before doubling his tally for the night. A Keylor Navas mistake allowed Blaise Matuidi to score the vital third goal, but Ronaldo's last-gasp strike ensured Madrid reached the semi finals, where they will face Bayern Munich.