In comics, Loki is nicknamed the God of Mischief for his casting of illusions. But is he really the God of Mischief in the comics, or is this simply a nickname given to him because he is the adopted brother and son of Thor and Odin, respectively (because Thor and Odin are gods)?
Yes. Well... No. It sort of depends on your definition of "Gods".
Technically, Loki is a Frost Giant of Jotunheim, which Marvel describes as
They are not actual gods.
Loki, however was adopted by Odin. Again, from Marvel:
Marvel explains Asgard:
They are not actually gods.
Marvel describes Thor:
To the Norse, Loki is a "God" - just as Thor and Odin are, but none of the Asgardians (much less the Giants of Jotunheim) are actually gods. They are powerful ancient beings with superhuman powers - but not gods.
In the comics, they are not gods. Not Odin, nor Thor, nor Loki.
This answer contains spoilers from Thor and Thor 2
This is explained by Odin in Thor, when Loki exclaims that he is a God and demands to be treated as such. Odin replies that he is not; that he was born, shall live, and shall die just like any mortal being.
Gods also can't be killed - at the very least it is extremely unheard of. In Thor 2: The Dark World, Thor's mother, Frigga, was killed by a stab while trying to protect Jane. Thor's companions are also near-fatally injured in Thor, but return for help soon enough that they are healed.
However, in Norse mythology, Loki is a god. He also helps others, but also causes problems. He usually appears in the form of a salmon, mare, seal, or even an elderly woman, as he is a shapeshifter (whereas in the comics and movies he is a Frost Giant). He is referred to as a trickster god.
In Norse mythology, Thor is the God of Thunder and Odin is the Allfather and ruler of Asgard, as he is in the Marvel comics and movies.
No, he's a giant (according to Norse mythology research I've done). He is also a "sorcerer", as he has the powers of a god, without actually being a god. He is commonly referred to as a god, but technically speaking, he's a giant.