Two OVAs released with the 8th and 10th volumes of the original novel. They fall chronologically between the first and second seasons. Season 1, Episode 13:
Haruna is given the task to hold a Spring Festival at the local shrine, in her own magical-Equipment-girl way, of course... Seraphim does not want to be a freeloader at Haruna's and Ayumu's place, so she starts cooking... And a concentration-game contest in the school's main assembly hall pushes Ayumu and Orito to their limits... (Source: AniDB) Season 2, Episode 0 part 1:
Haruna wants to play more with Hellscythe at a swimming pool.
Season 2, Episode 0 part 2:
Hellscythe's birthday is near! Haruna prepares a birthday party for Hellscythe in her own magical-Equipment-girl-way. What kind of party could Haruna be holding? What kind of birthday presents will Ayumu and gang give to Hellscythe?
Mr. Church reunites the Expendables for what should be an easy paycheck, but when one of their men is murdered on the job, their quest for revenge puts them deep in enemy territory and up against an unexpected threat.
In an alternate universe where twinned worlds have opposite gravities, a young man battles interplanetary prejudice and the laws of physics in his quest to reunite with the long-lost girl of his dreams in this visually stunning romantic adventure that poses the question: what if love was stronger than gravity?
Welcome to Rekall, the company that can turn your dreams into real memories. For a factory worker named Douglas Quaid, even though he's got a beautiful wife who he loves, the mind-trip sounds like the perfect vacation from his frustrating life - real memories of life as a super-spy might be just what he needs.