The MCU Fan's Guide to Norse Mythology
To be fair, Thor is two steps removed from its Norse antecedents. The movie is an adaptation of a comic, which itself takes a fair amount of Artistic Licence. Still, anyone looking to understand Norse Mythology by way of Thor should know the following:
Thor is the god of thunder. He has a hammer named Mjolnir, forged by the dwarf Sindri on a bet with Loki (not in the heart of a dying star). His hair is red, rather than blond. His personality is boisterous and beligerent, without the softening notes of kindness and chivalry he has in the movies. He is Odin's son, but by the giantess Jord, rather than Gaia. He isn't prince of anything.
Sif is Thor's wife, rather than his friend. Far from being an Action Girl, she's mainly associated with domesticity. The only significant myth about her is the one where Loki steals her hair and has to replace it. She's also a blonde, rather than a brunette: her hair, initially golden, is eventually replaced with a magic wig of actual gold.
Odin is the king of Asgard. He has a spear (named Gungnir), two ravens, and two wolves. He sits on a throne called the Hlidskjalf, from which he can see all that happens in the Nine Realms. He also has only one eye, but he sacrificed the other willingly in order to gain wisdom, rather than losing it in battle as is implied in the movies.
Odin is married to Frigg, but is far from monogamous. Besides his legitimate son, Baldur, he has also fathered numerous children by various women. How many is unclear, but "Son of Odin" is a very common title on Asgard.
Frigg (not Frigga) is Odin's loving wife, and queen of Asgard. She is not, however, the mother of Thor, nor of Loki. In fact, considering that Loki killed her (only?) son, she may be the person with the most reason to hate him!
Loki is not Odin's son, not Frigg's son, and not Thor's brother. He is a giant, but there's no reason to think he was ever in the dark about his parentage. The bit about him being Laufey's son is correct, but...
Laufey is not Loki's father. Loki's father is named Farbauti. Laufey is Loki's mother. How she came to be Gender Flipped is unclear, but it may have to do with the fact that in mythology Loki is consistently referred to as "Loki Laufeyson" — whereas most characters in Norse Mythology have patronyms, Loki has a matronym. Laufey also isn't king (or queen) of Jotunheim; the Jotnar don't seem to do monarchs.
Loki's personality is very different in the myths and the movies. While both Lokis have motives that are often fuzzy, Movie!Loki's primary goals are Odin's love and the throne of Asgard. Myth!Loki shows no interest in either of these things. His main motivation, at least in the earlier stories, seems to be mischief. He does a lot of things that don't make sense (like stealing Thor's wife's hair), apparently just for the fun of it. Later on, his motivation turns more towards jealousy and hatred of the gods, though whether this is because of their derision of him, their treatment of his family, or other factors entirely is unclear.
While Loki in the movies appears to be single and childless, Loki in mythology has had at least two wives and numerous children, half of whom are monsters. They include Fenrir (a giant wolf), Jormungand (a giant snake), and Hel (yes, that Hel). One of Loki's children who appeared in the movies is Sleipnir, Odin's eight-legged horse. That's right, Movie!Odin rides around on his own grandchild! Hela was turned into Odin's son and Loki and Thor's sister, and Fenris appeared without a reference to his parentage.
Loki isn't known for illusions per se, but like his movie counterpart he uses trickery and cunning rather than physical force. He can shape-shift into various animals, is fond of cross-dressing, and has been pregnant on more than one occasion. For different reasons from the movies, Loki is also something of a Jerkass Woobie: he is constantly having painful or humiliating things happen to him, often to the gods' great amusement.
Heimdall is the guardian of the Bifrost, a.k.a. the Rainbow Bridge. There's nothing in mythology about him having golden eyes, but he does have golden teeth! He's also known (ironically enough) as "The White God".
The Warriors Three are pure Marvel invention. There are, however, numerous other gods on Asgard, including Tyr (the god of war), Frey (the god of fertility), and Freyja (the goddess of love).
As in the movies, Asgard is one of the Nine Realms. The other realms are not all named, but they do include Jotunheim (home of the Jotnar), Vanaheim (home of the Vanir), Svartalfheim (home of the Dark Elves), and Midgard (Earth). These realms are all connected by the roots of the World Tree, Yggdrasil.