\^o^/ Yay, the Loki thread is revived! <3
Spiritsword is most correct - the first series, Matantei Loki, was originally published by Square-Enix/GanGan comics (even though recently Comic Blade has gotten the rights to publish Matantei Loki - hence, MLR is published with spiffy black covers while ML has spiffy white covers)...I still don't think they should have released the 2nd series before the first. =o= Fools.
At any rate, if you want a firmer grasp of what's going on in the 2nd series, maybe try looking into the MaLoki anime - I think they're releasing it sometime in the very near future. (I can't wait! x3) It isn't exactly like the manga, but it does give you the basic relationships between the characters and such, which is what I gather makes picking up the 2nd half of the manga so confusing. ^^;
As for characters...I'll always love Heimdall. He's such a creepy little psycho, it's hard not to appreciate his madness, though I'm also quite partial to Loki and Narukami-kun. x3
EDIT: decided to do a basic...character chart thingy. XD; There may be spoilers below, but I tried not to give away anything that wasn't already in the first 2 volumes of MLR.
Loki: Main character, banished to Earth (why Japan of all places still escapes me. XD; ) by Odin for reasons that I believe are revealed in the last book of the series. He runs the Enjaku Detective Agency...and his shikigami (the small pink floaty thing that follows him around) is called either Ecchan or Punyan-san (NOT Pmeow...how do you even SAY that? o_O)
Mayura: a girl who's obsessed with mysteries and detectives who follows Loki around and admires his detective skills. She's annoying and air-headed, but she's got a good heart. I think.
She's not in any way related to Norse mythology, she's just there to look cute. XD Everyone likes her, and Freyr wants to take her as his bride. Freyr doesn't know what he's getting himself into.
Yamino-kun: Loki's attendant/butler/chauffer/cook/maid. [spoiler]Yamino is the Midgard Serpent Jormungand in disguise, Loki's 2nd son. In Norse mythology, the Midgard Serpent was chained underneath the sea, and there grew large enough to encircle the earth.[/spoiler]
Narukami-kun: The Norse god Thor. In the first series Narukami was originally sent by Odin to assassinate Loki, but decided against it when he realized that Loki wasn't evil - In Norse mythology, before Loki grew evil and was chained by Odin, he and Thor were close friends and there are quite a few stories of heroic deeds they preformed together. In both the manga and the anime, Narukami-kun gets trapped on earth and ends up attending high school, living in a one room apartment, and taking up countless part time jobs.
Heimdall: Heimdall was also sent by Odin to assassinate Loki, but unlike Narukami-kun he doesn't really have any intentions of giving up. Heimdall blames Loki for the loss of his right eye (note in Norse mythology it's Odin that has one eye and not Heimdall, and Odin's eye wasn't stolen by Loki) and wants revenge. Lots of revenge. Heimdall is freaking insane, lives with Freyr, and goes by the alias Higashiyama Kazumi (obviously a tribute to Higashiyama Kazuko, the co-author of Tactics).
Freyr: Freyr too was sent to kill Loki, and like Heimdall wishes to do it out of revenge for his sister Freya, who was also banished to Earth after she attempted to stand up for Loki. In the first series Freyr decides that, since Loki is a detective, he should be the natural enemy of a detective - a phantom thief (kaitou). Freyr isn't very bright. He has a flying mechanical pig named Gullinburusti (a golden boar given to him by the dwarves in Norse mythology) and a large flying ship that has a name that escapes me at the moment. XD;
Freya/Reiya: As afforementioned, Freya was also banished to earth in the form of a little girl. But unlike Loki, as her child form, Reiya, Freya has no memory of her position as a goddess. She does, however, frequently transform back into her adult self to go chase Loki about, attempt to wed the poor detective, and try to hitch cats to sleds.
I'll post more about Odin, Spica, the Norns, Hel, Fenrir, and Utgard-sama later. XD;