Here's how to solve the riddle: watch the end and then go back and watch the first 15 seconds. Mostly everything you need to know takes place there, but I'll break it down anyway.

French aristocrat Cossette falls for Marcelo, an Italian artist who stays with her family. He find her to be the epitome of Beauty and paints several portraits of her. She falls for him, of course, and the two become engaged (why her family allows her to take up with a mooching artist I don't fully understand - he wasn't a particularly good one). He loves her as well, except what he loves is her beauty and youth, not who she really is.
So, inevitably during the course of his last portrait he fall madly in love - with his work - and oddly it reciprocates. He decides once it is finished that he cannot abide to her growing older and he slaughters her and her whole family so that she will remain forever young and beautiful.
That's just fucked up enough for her to become a vengeful spirit that eventually finds our protagonist (he's Marcelo's reincarnation - SURPRISE!) and bequeath him with the Eternal damnation of pain and suffering (FUN!) through the 'memories' of the objects that witnessed the betrayal so long ago (she has very loyal cupboards). Each one witnesses said betrayal from a different perspective and so keeps a different 'memory' of what happened, who whom and forms an opinion of how badly the protagonists should suffer because of it. Protagonist is a masochist with Stockholm Syndrome, so he naturally falls deeply in love with his imaginary tormentor. Keep in mind that however dark or surreal this anime becomes it is still a Magical Girl series at heart, so keep an eye out for the twisted transition "quick change" sequence (please see Hell Girl for another example of this art form).
Later, when we get to the clock phase we see Cossette grow older, which is an interesting plot 'twist' and Eiri Kurahashi (protagonist torture unit) states that he loves Cossette and will no longer fight against the torture since it means being with her (he is related to a madman, it's just a different kind of crazy here).
Later she falls in love with him and decides that she doesn't want him to suffer the way Christ did and decides to leave the poor man be. This is where it gets even more fun!
So, remember the painting that Marcelo was so madly in love with? Well, it turns out it reciprocated with the passion of 1000 firey suns. And not only that - it's the jealous type! So we discover, far too long afterward, that Kurahashi was tricked into thinking Cossette came back for him and decided to love him for eternity. Except it was the painting the whole time, angry and jealous that Marcelo's reincarnation loved the real Cossette instead of it. But once he figures it out he beats it pretty quick - how one might ask? Well that's easy, he just says he implies that he loves the real Cossette for who she is and then paints her portrait with his own blood (still related to Marcelo, still crazy). This is apparently a "warmer" likeness and so it defeats the evil painting, thereby taking out the dreaded curse and it is implied that everyone lives ... surreally ever after.

So, I forgot to mention it but there's a "love interest" (by love interest we mean she loves and he's obviously not interested as he has fallen for Dorian Grey's prototype). She pretty much only comes in to shout his name and get angry at him. And her age seems to change as often as her name does; I spent most of the anime thinking she was his mother or older sister or something and if that wasn't confusing enough different people refer to her by different names (family + given) and the way it is executed meant I spent the whole anime thinking there was "Mataki - her" the older cranky aunt and "Shouko" a faceless fellow student (same age) who loves him. Little did I know they were the same person the whole time!! And not only that - it turns out that she is the reincarnation of Cossette (or at least she becomes her later - it isn't clear which).