The references are as follow. I'll divide it into its categories. Also note that I'd refer to SAO as ALO here since the story takes place in Alfheim Online and not Sword Art Online's Aincrad.
Alfheim (Norse: Álfheimr) means the land of fairies. This is the world where the players live. Funnily, the races that live in this land are not from Norse mythology, but is actually from England, Ireland and Scotland, with the exception of Salamander. More about the races in the races section down below.
Jotunheim (Norse: Jötunheimr) means the land of giants. The creatures that live here are the giants. Tonki (Jellyfish Elephant, Kuzuha/Leafa's friend/pet(?)) is one of those giants.
Nilfheim (Norse: Niflheimr) is the land of ice and snow. It is referenced in ALO as the cause of change in Jotunheim, that is the outbreak of ice giants from Nilfheim, which is located under Jotunheim, cause the change in Jotunheim's once green lands to that of ice and snow.
Muspelheim (Norse: Muspelheimr) is land of fire. In ALO it is located under Nilfheim.
Yggdrasil (Norse: Yggdrasil) the three that connects the 9 worlds according to Norse mythology. Out of those 9 only Alfheim, Jotunheim, Nilfheim and Muspelheim mentioned in ALO. Out of those 4 only 2 (Alfheim and Jotunheim) are actually shown.
Thor (Norse: Thor) the god of thunder, wielder of the magic hammer Mjolnir, son of Odin.
Freya (Norse: Freyja) is a goddess associated with love, sex, beauty, fertility, gold, seiðr, war, and death.
Thrym (Norse: Þrymr) is king of Jotunheim. In ALO he is a king of Nilfheim who invaded Jotunheim along with his ice giants.
Excalibur is a sword belonged to the legendary King Arthur of England. It is also one of the sword featured in many video games, mainly Final Fantasy. In Final Fantasy series it usually is one of the strongest swords. In ALO it is a sword promised by Thrym as a prize for slaughtering the original dwellers of Jotunheim (Tonki's race).
Mjolnir (Norse: Mjölnir) is a magic hammer of Thor, capable of summoning thunders.
Thor missing his hammer is one of Norse legends, where Thor lost his magic hammer Mjollnir. It was said that his hammer was stolen by the king of the Jotun, Thrym. Thor, although reluctant, agreed to Loki's suggestion to dress as Freyja in his attempt to get the hammer back. Thor later killed Thrym and get his hammer back. This is referenced in ALO with Klein finding a female NPC with HP bar locked in a prison made of ice. Later during the fight between Kirito's party and Thrym, the said female NPC revealed himself to be Thor. Thor then killed Thrym much like in the legend.
Races (Bonus Section)
Cait Sith in its original myth stole people's soul before they are collected by gods upon their death. In ALO, they are beast tamers. Silica and Shinon are Cait Sith in ALO. Cait Sith originated from Scotland.
Spriggan are small fairies said to be guardian of treasures. They are said to be mischievous. It has the ability to transform into huge creature. Kirito is a Spriggan in ALO. Kirito also used a transformation magic to transform into The Gleam Eyes which is a reference to this ability. Spriggan in ALO also known to be very useless in magic due to their magic being mere illusions (reference to their magic being for mischiefs).
Gnome are small, humanoid Earth fairies. Gnome in ALO are known to be master miner. Agil is a gnome.
Imp are small goblin like creature. Imp in ALO are not very well explored with the only known Imp is Konno Yuuki/Zekken.
Leprechaun in its original myth are said to have hid a pot of gold at the end of a rainbow. Lisbeth is a Leprechaun in ALO.
Pooka originated from Ireland. Pooka or Púca means ghost or spirit in Irish. It is not well explored in ALO. Sasha is a Pooka in ALO.
Sylph are wind spirits. Sylph in ALO are master in wind magic. Sylph is also the race that has the most known characters. Lady Sakuya - Lord of the Sylphs, Leafa, Recon, Sigurd (Exiled), and Erika (Asuna's alter account) are Sylphs.
Undine are water spirits. Undine in ALO are also master of water magic. Asuna is an Undine in ALO.
Salamander in ALO are known to be master of fire magic. This is a reference to a type of salamander (animal) that is resistant to fire, called fire salamander. Salamander in ALO is unique in that it is the only race not based on English, Irish, or Scottish myth. Klein is a Salamander in ALO.