Elluka as she is seen in "Chrono Story"
Elluka Clockworker is an immortal witch. She is asked by the Tree of Eldoh, an old friend, to retrieve the Seven Deadly Sins, and she agreed. In her past, she was engaged to Kiriru Clockworker, but in a tragic turn of events, she killed Iriina, his sister with whom she had a rivalry with, and Kiriru is presumably driven insane. It is unknown if this has anything to do with her immortality. 
In her quest to gather the seven sin vessels, she possesses both Lukana Octo and Kayo Sudou, to get the "Venom Sword" and "Blood Stained Scissors" respectively. Little is known about how she possesses her victims, and to what extent.
Featured in...
Chrono Story
In Chrono Story, the Tree of Eldoh answers the pleas of Hansel and Gretel, asking Elluka to retrieve the Seven Deadly Sins. Elluka agrees, stating that she has unlimited time, anyways, and doesn't mind collecting the sins if it keeps her entertained. The song goes on to hint at her past, stating that she lost her loved one and that she destroyed something precious. For this reason, her gift immortality is an empty victory. It is clear that she was once in very high standing, and somehow lost it all. The song ends with her finding the Duke's castle, giving a few of his victims brief cameos.
Recollective Musicbox
Recollective Musicbox sheds more light on Elluka's past. It speaks of Kiriru Clockworker, a respected musicbox maker engaged to Elluka. He begins to make a beautiful musicbox for her and his sister, Iriina. The two girls were close friends, until both were chosen as potential rulers of the kingdom for their magic skills. Pitted against each other, they begin to hate each other. One day, Kiriru comes home to find his half-made music box covered in blood, with one girl (presumably Elluka) crying and the other (presumably Iriina) collapsed, apparently dead. The act apparently ruins the country and drives Kiriru insane.
Princess Sandman's GIFT
Elluka makes a brief cameo at the end of Princess Sandman's GIFT, sharing a conversation with Gumilia. Gumilia informs Elluka that the sin vessel (the clockwork doll, although it is not stated outright) could not be retrieved. Elluka responds by saying that they will have to look deeper into the mysterious "Pere Noel," and the two head out to Lucifenia.
Five the Peirrot
In Five the Peirrot, Elluka tries to convince Hansel to escape with her. Hansel instead betrays her to Julia, and Elluka flees. Later, Gumilia shoots the boy, and Elluka tells him that he should have escaped with her.
Cappricio Farce
Elluka makes a cameo in here, although she is in Kayo Sudou's body. She operates under the name "Ma," short for "magician." The Master of the Court calls upon her, asking where the remaining vessel (presumably wrath) is. She states that she doesn't know where it is, but that she fears that it may be in "her" hands (presumably the Master of the Hellish Yard).
Connections to Other Characters
Eldoh: An old friend of hers who asks her to track down the Seven Deadly Sins.
Lukana Octo: Elluka possesses her using the "body swap" technique in order to get the "Venom Sword," which is the vessel for lust. It is unknown how long she possessed Lukana for, or if she is the one who concieved Gammon Octo's decendant.
Kayo Sudou: Elluka possesses her using the "body swap" technique in order to get the "blood stained scissors," the vessel for envy. It is unknown if Kayo commited the murders before, after, or during the time that Elluka possessed her, or if it was actually Elluka herself who commited the murders.
Gumilia: Her apprentice, who joins the Pere Noel with her. She was a spirit, until Elluka gave her a physical form, resembling Gumina Glassred's.
Michaela: Was given a physical form by Elluka, resembling Eve Moonlit's.
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