Mythical Detective Loki Ragnarok/WMG

This series is the prequel to Ah My Goddess, or vice versa

 * Which would make AMG the Lighter and Softer version of Loki, or Loki the Darker and Edgier version of AMG.

Mayura is the Reincarnation of Sigyn, Loki's Goddess wife
Odin did nasty things to Loki's entire family to get rid of them. However, their Jotun heritage made it difficult to get rid of them entirely. Loki's Jotun wife, Angrboda; reincarnated as Spica, appears in the manga. Sigyn, however, is a mystery in Norse Mythology since there's practically nothing mentioned of her except for her loyalty to Loki. She was a goddess, but apparently not important enough to be the goddess of anything in particular. Thus, Odin was able to simply kill her. Odin may be aware of who Mayura is; since when he taunted Loki by possessing Mayura, he had her wearing a wedding dress and wearing a locket with his face on it.

Kotarou is the reincarnation of Baldr.
This one nobody seems aware of, but it would be ironic; and he always seems to be around for some reason.

The averted fight with Odin over dominance for Asgard would have been Ragnarok.
That is why Loki deciding he had people he cared about in the human world was avoiding it.