Sharon is Slayer's wife, and apparently immortal and invincible; for one thing, she can survive getting drained of blood by Slayer without any apparent lasting effects (one of Slayer's opening scenes before a battle shows him completely draining her). In one of Eddie's endings, Eddie melts after attempting to possess her, and I-No (who set him up to this) comments, "Illness, parasites... Nothing sticks to her." Sharon's exact nature remains unknown. She is also known to become violently jealous and possessive whenever she sees Slayer conversing with another woman.
It was later confirmed by Daisuke when he was asked that she's just a human but with physical idiosyncrasy, which means that there's perhaps a bug in the information contained in the Backyard that allows her to be such an ageless and death-less woman.
Her name is almost certainly a reference to Sharon Osbourne, the wife of Ozzy Osbourne, also known by fans and the media as the "Prince of Darkness"(a title typically attributed to vampires in various media).