Just so we are all on the same page, let's start with just who the Norsemen are. If you have the stereotypical vision of a Viking in your mind then you're on the right track. We are basically referring to the Scandinavians of medieval times who set the tone for exploring, colonizing and flat-out raiding from the sea in their wooden longships. They lived in harsh and extreme conditions: months of extreme cold, surrounded by snow followed the midnight sun and a short but beautiful summer. Given the environment in which they lived and the intensity of the seasons they experienced it is no surprise that two elements played key roles in their mythology: ice and fire. Nature, in general, must have been both beautiful and fearsome to the Norsemen. The majority of our impression of the Vikings is probably not accurate. Most envision Vikings as lawless, dirty, blood-thirsty barbarians incapable of any sort of civilized behavior when, in reality, they were quite the opposite. The contemporaries of the Vikings saw them as a culture to be feared but also revered. Their strength and fearlessness in battle are legendary so it is no surprise that a group of travelers who faced death from their environment and from their constant battles would love a god that was fearless and strong, the god of fertility and the protector of Earth: Thor, god of thunder.
So, finally, to the point of this, where do Thor, and the other gods of the Norsemen, find common ground with their mythological counterparts? Let's take at where Thor, Odin, Loki, Sif and the evils of Norse Mythology fall onto common ground with Marvel's take.
So long as we're all being honest here: Tom Hiddleston's Loki is THE best thing to come out of the MCU thus far. Hiddleston has given Loki, an original villain of the Marvel comics, new life and is probably the most popular character Marvel Studios has produced (not named Tony Stark). As many of you know, Hiddleston actually auditioned for Thor and, I imagine, nothing in the MCU would have been the same had he won that role and not been Loki. Hiddleston's portrayal of Loki has been magnificent and I look forward to Thor: The Dark World more for what it is Loki will do than Thor. Loki has long been a pain in Thor's side in the comics and, like his MCU counterpart, can never be trusted. So, to the point, how does Marvel's Loki compare to his mythological counterpart? Let's drop them into a Venn diagram and find an answer.
Loki's rise in popularity, as I explained above, is, no doubt, due to the brilliant performances by Tom Hiddleston as the god of mischief. The MCU version of Loki is not all that far removed from its comic book companion, though the likelihood of MCU Loki having as long of a shelf life as comic book Loki is unlikely. Loki's Marvel comics appearances date back to 1949, before Marvel was it's own entity. In 1962 Loki made his "official" Marvel debut and, in 1963, it was Loki's mind-control over the Hulk that brought together a group of Earth's Mightiest Heroes for the very first time. So, depending on which math you choose to do, Loki has been in Marvel comics for 64 years and plenty of adventures!
Loki, as seen in the film, was the son of Laufey, king of the Frost Giants, the sworn enemies of Asgard. After defeating the Frost Giants, Odin (father of Thor and the All-Father of Asgard) found Loki, hidden away in shame over his stature: even as a baby Loki did not possess the formidable size of other Frost Giants. Odin, in obedience to his own father's final request, took Loki to Asgard to be raised as his own son.
Despite Odin's efforts to raise Loki as his own, Loki must have always sensed something was not quite right and was, from the very beginning, jealous of Thor and the attention and adulation with which he was showered. In fact, if you've ever thought to yourself, "Man Thor's hammer looks silly with that way too short handle," well, you'd have Loki to thank for that. Jealous that his brother would have such a mighty weapon, Loki schemed to make it his own and went so far as to impede the progress of its creation, ending in it the short handle for which it is famous. This is just one example of Loki's schemes as a little tugger and those schemes, and his jealousy and hatred for Thor only grew, until his penchant for mischief led him to be imprisoned by Odin...and you'd have to imagine that didn't sit well.
As a boy, and into adulthood, Loki practiced sorcery and eventually became a master of it; however, Loki's focus on the dark arts of sorcery would ultimately lead him to become the god of evil and to formulate many schemes and create many alliances that he hoped would bring Ragnarok, the final battle that would culminate in the destruction of Asgard.
As seen in Thor, it was not until Odin banished Thor to Earth in an effort to teach him humility, that Loki was able to truly engineer machinations that would, in his mind, lead him to the throne of Asgard, placing him above the brother by whom he had felt so slighted as a child. Almost cyclically, Loki would take the throne during the Odinsleep, only to surrender it back to the All-Father. Simultaneously, Loki would often, despite his regret over his role in the creation of the Avengers, scheme against and attack Earth for no other reason than to infuriate his brother who was the champion of Midgard.
Despite several redemptive character arcs, Loki was never to be trusted and could, seemingly despite his nurturing as an Asgardian, overcome his true self. He entered into partnerships with several of Asgard's most hated foes, Malekith and Surtur to name two, and was never able to fully give up his villainous, scheming ways. Loki is one of the GREAT Marvel comics villains (number 9 on comicvine.com's list of baddies!!).
Turns out that the Loki of Norse mythology is just about as big of a pain in the arses of the Asgardians as he is in Marvel comics...depending on who you ask! Suffice it to say that Loki, in the mythology of the Norsemen, is the most confusing and complex of the gods. He ranges from the fire god to the god of mischief and is either helping the rest of the pantheon defeat a scheme or scheming against them for his own ends.
To be sure he is a jotunn, or frost giant, but is still associated with fire. In some respects, Loki is associated with the Christian ideal of Lucifer: evil, able to shift shapes and manipulate to his own ends despite never truly seeming evil. Suffice it to say that Loki, is THE most confusing mythological character I've ever encountered. He is both good and bad, mother and father ( I mean that), destroyer and creator. In some versions he is the brother of Odin; in others his adopted son, as in the comics and MCU. I prefer to say the following in summation of the reading: Loki is symbolic of the dual nature of man and that is something so very important to any culture. He is neither fully good nor fully evil, yet capable of both. Loki is the necessary evil of Norse myths but gives the people the idea that, at times, anyone can be redeemed. If Loki and Odin are brothers, they are yin and yang...one could not exist without the other. Loki is all things complex and inexplicable and the Norse were lucky to have him.
Verdict: Venn diagram nearly impossible with Loki because there is either too much or not enough info. Sorry for the poor verdict but, hopefully, the information helps us see this god as we want to...which may just be the point!