The World God Only Knows has four original video animations (OVAs) that were released with limited editions of certain volumes. Most of them are adaptations of chapters in the manga that wasn't in the seasons themselves and serves to further expand on the events referenced within the episodes.
4 Girls and an Idol (2011)
4 Girls and an Idol is an Original Video Animation released with the limited edition of the 14th volume of the manga. Adapting two chapters (54 and 55) of the manga, it tells the tale of how the band 2B-Pencils, comprised of Chihiro, Ayumi, Elsie and Miyako, with Yui joining up after the events of this OVA, come together. There are two new character songs serving as the opening and ending, and both are great. Throw in the appearance of Kanon, a slew of humor and an excuse for Keima to appear and tutor the girls, and you have an excellent episode. The main plot here is that in order to secure a club room for the Light Music Club, and thus an excuse to practice during and after school, they have to get 100% in their English exams. Enter Keima and his godlike ability to get 100% in exams, imparting some of his knowledge. Getting 100% sounds impossible and the way this plotline is resolved in the end was funny and elegant.
Reunion (2012)
Reunion was released with the limited edition of the 19th volume of the manga an dis the first of a two-part OVA adapting the Tenri arc. The summer vacation has begun and Keima is hyped with the fact that he is able to game for 100 hours (and even warning his mum that he will disappear until the end of August). However, this is dashed when his supposedly childhood friend and neighbor from ten years ago, Tenri, arrives. Tenri herself is shy and timid, but it is a shock that Keima doesn't remember her at all. Naturally, Tenri becomes a target as she is hosting a loose soul, but this loose soul seems to act differently and having a personality of its own (which will later be explained within the third season). Compounding the problem is another demon, Nora, appears and claimed the assignment of Tenri's loose soul as her soul, with the misguided intention to kill Keima. The pacing of this OVA is quite slow at times but once again, the humor is solid and the ending is intriguing.
Chance Meeting (2012)
Chance Meeting is the second of a two-part OVA adapting the Tenri arc, released with the limited edition of the 20th volume of the manga. Continuing from the end of the previous episode where Keima remembers that he and Tenri had explored the underground tunnel before in their youths, the mysterious being within Tenri is slightly explained. It feels like your typical episode, but there is a tiny twist in how it ends with the lost soul being captured by the new demon Nora. There's less humor in this episode and more seriousness, as well as a lot of foreshadowing for the events of Season 3. Nevertheless, it was still enjoyable.
Magical Star Kanon 100% (2013)
Magical Star Kanon 100% is the fourth and final OVA released with the limited edition of the 22nd volume of the manga. No surprise that it stars Kanon. Elsie also plays a big role when she finds out auditions are being held for the role of Kanon's sister. However, a loose soul throws things out of whack and turns Kanon into a little girl again. The episode revolves around how Kanon turns back to her normal self and uses the power of her voice and songs to capture the loose soul. It's basically an episode to show how awesome and cool Kanon is and it succeeds. The pacing can be a bit slow and the plot cliched but Kanon is such a likeable character that it doesn't matter. The new songs aren't as good as past ones but the music overall is still fantastic.
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For other animation reviews, have a look at this page.