The original origin, which was believed by most Asgardians (if they even believed the Disir were real in the first place), is that when Bor was a young god, the Disir were to him what the Valkyrie were to Odin. They had rebelled against Bor and started to feed on other Asgardian Gods. When Bor discovered what they were doing, he cast them out of all the realms, to exist in the spaces in spirit alone. They were cursed to remain forever hungry and feed only on the spirits of Asgardian Gods, for they would only be in Asgard or Hel. They could not eat anything they themselves killed.
Later their real origin came out. The Disir were held very closely under the thumb of Bor, and disliked his extreme control. Once, Bor left them to guard his home, and Sigurd and a group of his mercenaries, who worked for Bor, came along. The women were attracted to the men, and slept with them. When Bor returned he found them all asleep. He killed Sigurd's men but when Brun stood against him he cursed her. Her and her sisters would be forced to roam the middle life only able to eat the spirits of Asgardian gods, until they killed Sigurd or he wedded them.
There were originally thirteen Disir. Two were killed recently, leaving eleven.
Only four of the Disir have been named. They are Brun, the leader, or first sister; Kara of the Twilight, Brun's favorite sister, who often uses a bow and arrows; Gondul the Fool, who is often less courageous than her sisters; and Hlokk the Mad, who is both more insane and bloodthirsty than the others.
Major Story Arcs
Deal between Loki and Mephisto
Ages later, Loki summoned them in Latveria. By using the blade Eir-Gram he managed to get the Disir to submit to him. He made a deal with Hela, who no longer had her own realm, that he would give her a realm if she would spare his soul. After she agreed, Loki showed Mephisto the power of the Disir and gave them to the dark lord in exchange for giving Hela a portion of his realm. The deal was made, Mephisto gave a portion of his kingdom for Hela to govern for a thousand and one years in exchange for the Disir's service to Mephisto for a hundred and one days.
During the Siege of Asgard, the Disir attempted to devour the souls of the fallen Asgardians but Hela had sent Danielle Moonstar, a former mutant who had owed her a favor, to guide the fallen Asgardians to Hela's realm as a Valkyrie.
Following the Siege of Asgard, the Disir put down a rebellion of demons. The Disir desired to attack Hela's realm. To circumvent Bor's curse they convinced themselves that Hela's new realm was not the Asgardian Hel, but a different realm all together. With Mephisto's indifference they attacked Hela's Valhalla devouring many of the Asgardian souls. Hela attempted to stop them with the Eir-Gram blade, but was overwhelmed by their combined fighting ability and the blade was stolen. Brun even cut off her hand, which eventually became Leah. To protect the souls in her charge she turned herself into a fortress with the souls inside to delay the Disir. She contacted Asgard and pleaded for aid. Thor and Tyr were sent to find a solution. Tyr protected Hela while Thor sought the Eir-Gram in Mephisto's Realm. Thor was able to retrieve the blade and gave one of the Disir who had come to stop him a choice: admit they had broken their oaths or die another death. The Disir admitted forcing the Disir to leave Hela's realm and possible even destroying them. Afterwords, due to "dying" again in Mephisto's realm they became subject to Mephisto and transformed into a ring on his finger. The implication being Mephisto allowed events to transpire due to no matter who won in the end he would come out ahead.
When Hela learned that Mephisto had control of the Disir, she became enraged, but Loki calmed her down and made a deal with Mephisto. Loki had been reborn since Siege and was trying to do good deeds for all the evil he had done previously. The deal included many things but important to the Disir was that Hela would take control of all but four Disir. Loki would take Brun, Kara, Gondul and Hlokk with him to stop The Serpent and in return he would give them their freedom from his control. After their mission was completed Loki gave them there freedom but then Mephisto took control over them because they had died in his realm.
In the aftermath of Fear Itself, the Disir were seen in Mephisto's hell being tortured, biding their time, and planning their revenge.
Sigurd, the Asgardian hero whose dalliance with the Disir had cost them their "humanity," had gone to Earth and hidden among humans for millenia. He lived in San Francisco, bedding human women and living a care-free life. However, when he saw the New Mutants lived next door, he recognized that Dani Moonstar was a Valkyrie and thought that the Asgardians had finally found him. He rushed to his secret hiding place and put on his armor, preparing for a siege.
The New Mutants actually had no idea that he was there, but when he put on his armor, the Disir were suddenly able to sense his presence. They transformed into demonic forms and escaped Mephisto's hell, planning on killing Sigurd. They came to Earth and wreaked havok. Sigurd was ready for them, however, and cast a spell that made them (and a number of other Asgardians) think they were normal humans. They lived as members of a anorexia support group for a while, until one finally ate a cat. Then they all turned their bloodlust back on.
Finally Dani Moonstar told Bor that they knew where Sigurd was, and that he would marry the Disir. Bor came back to Earth to officiate. Sigurd really wanted nothing to do with this. Eventually, there was a fight, and Bor was cut. The blood then made the Disir go after him, and he had to agree to lift their curse to get them to stop. All of this was according to a plan of kid Loki's, so they were in his debt once again.
After their curse was lifted, Hela offered to let them serve as her Valkyries, and they accepted. They visited Sigurd to let him know that they were not going to kill him: as Valkyries they now knew the time and place of his death, and would meet him then.
The Disir recently helped Loki as he tried to gain entrance to Hel, during the Everything Burns story arc.
The unusual nature of the Disir makes them incredible difficult to fight. They exist as some sort of living/dead spirits with both a spiritual and physical presence. As former Valkyries they possess some degree of superhuman abilities. They are experts in Asgardian warfare. They seem to each be trained in specialized skills. Gondul has demonstrated great knowledge and the ability to use magic, especially teleportation warps. Others tend to focus on specific weapons. Their deadliest skill is their teamwork. Together they can overwhelm beings who one on one would be too much for them. However, if they do not utilize team work they can be defeated as in the case with Loki.
As the Disir they are immune to normal weapons and highly resistant to magical weapons and magic. Mjolnir was barely able to physically effect one and could not damage them. Kelda's magic was thought able to slow them down, but not stop them. The Disir can render themselves intangible to physical assault and pass right through physical objects. Hela was able to make magical weapons that she gave the New Mutants, and which they were able to use to hurt and capture the Disir. Heavily enchanted demon blades were thought to be able to hurt them, but it is unknown if they could. This combined with their fighting abilities makes them nearly invincible as a team.
At one point, they were able to travel directly through Tyr's body, as if they--or he--were intangible. It's unclear if this was a power of theirs, or whether Tyr, as a dead soul in Hel, was not fully tangible for some reason, but since he seemed to be tangible otherwise, it was probably an ability of theirs.
They have also shown the ability to combine together into one giant being, which is presumably even more powerful than they are individually.
Perhaps most dangerous of all is the Disir can appear to anyone who speaks their name, quickly strike them down, and return from whence they came regardless of space or dimensions. Because of this, Asgardians are very fearful and careful not to speak their name.
Despite their fighting abilities and unique nature the Disir have two major weaknesses. First, they were bound by their oaths and the curse of Bor. If they broke their word or violated the terms of the curse they would be destroyed. However, this curse has now been lifted. They also could not break their oaths to Loki or Mephisto. Second, they are vulnerable to the soul of other beings. Tyr's use of his own soul as a weapon was able to cause them pain. The Eir-Gram sword was empowered a fraction of Kelda's soul stolen and design to draw out the soul of the wielder into the blade. This combined with the powerful magics forged by Loki into Eir-Gram by the fires of hell itself make it the only known weapon that can kill the Disir.