OVAs bundled with volumes 42, 43 & 46 of the Aa! Megami-sama! manga. 

An Angel Eater has been freed in Heaven. Since Goddesses and Angels share body and soul, losing your angel results in going into shock for the Goddess. Lind goes to Earth to protect Belldandy and the others unknowing that it is a trap.
 
(Source: Anime News Network)

Alone in his dorm on a Saturday night, Nekomi Tech’s Keiichi Morisato dials a wrong number that will change his life forever—reaching the Goddess Technical Help Line. Granted one wish by the charming young goddess Belldandy—a wish for anything in the world—Keiichi wishes she would stay with him always! Complications are bound to ensue from this; the immediate first being the new couple getting tossed out of the dorm—it’s males only! 
As the hapless student and his mysterious “foreign beauty” ride around looking for a new place to stay—risking the different dangers of seeking shelter with an otaku convinced Belldandy is an imaginary woman, and a Zen priest convinced she’s a sinister witch—Keiichi’s still got his classes on Monday morning! How is his new “exchange student” companion going to be received on the N.I.T. campus? A little too well for normal life to ever return... (Source: Dark Horse) 
Note: Won the Kodansha Manga Award for General Manga in 2009.

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