Omake Special from the final DVD volume. The Special storyline has very little to do with the original series outside of having some of the same characters, and has a completely different storyline which does not fit into anything which came before it. (Source: AniDB)

Koyomi Araragi is studying hard in preparation for his college entrance exams when he begins to notice something very strange: his reflection no longer appears in a mirror, a characteristic of a true vampire. Worried about the state of his body, he enlists the help of the human-like doll Yotsugi Ononoki and her master Yozuru Kagenui, an immortal oddity specialist. Quickly realizing what is wrong with him, Kagenui gives Araragi two choices: either abstain from using the vampiric abilities he received from Shinobu Oshino, or lose his humanity forever.

As part of a mysterious contract agreed upon by a goddess and his parents years ago, Makoto Misumi finds himself sent to another world to meet the goddess and become the hero. However, the deity deems Makoto to be hideous, refusing to even lay eyes upon him and revokes his heroic title. Disdainfully giving him the ability to understand all languages except the human language as compensation, the goddess drives Makoto off to the farthest edges of the wasteland, far from human civilization. Due to the disparity between Earth and this new world, Makoto's inherent physical and magical capabilities awaken, making him extremely powerful. He meets various demihumans and mythical beings who all end up being captivated with his characteristics and join Makoto in building a new community where all of them can peacefully coexist. Nevertheless, despite this success, Makoto still yearns to meet fellow humans. In a world where the goddess herself has barred him from interacting with his kind, it is up to Makoto and his companions to fulfill his desire—and perhaps reform society along the way.

When ordinary boy Kagami Kazuya meets the beautiful tsukumogami Kiriha, his life gets turned upside-down. As a Taboo Child who draws the supernatural towards him, he receives orders from the God of the Land, Kukuri, to become an exorcist and defeat these evil forces. And so, he and Kiriha do battle. To find out information on these supernatural beings, Kazuya and his friends set up a counselor's club at school. But behind the typical-seeming troubles he hears about, he uncovers a major plot to target Kukuri... In addition to the sadistic-yet-beautiful tsukumogami Kiriha, the situation draws other girls to Kazuya to join the fray! (Source: Crunchyroll)