Most know Loki as the adopted brother of Thor from the Marvel cinematic universe and actually know very little about Loki's true story. Hailed as the 'mischievous one', Loki is the magical, shape-shifting, gender-swapping, Jötunn ('giant'). His name crops up in just about every sketchy situation the Æsir (Old Norse for 'Gods') find themselves in throughout the legends of Norse Paganism. Since he was always in trouble with the ancient Gods and Goddesses and also a Jötunn, many modern believers (a.k.a. Heathens) dispute his status as a Norse God but have grown to accept his place in the pantheon. After all, Loki and all his children played some very crucial roles throughout the myths. Only there was something very odd about the family of a magic-using, giant from Norse mythology that even the Æsir themselves feared most of his offspring.
1) Nari and/or Narfi – Loki's family started off innocent enough with his son of two names, Nari or Narfi, born of Loki's wife Sigyn. Not much mention was made of this son of Loki except that Nari eventually took a wife and they had themselves a daughter by the name of Nött ('Night'). This made Loki the grandfather of Night. It did not end there because Nött found a husband named Delling ('daybreak') and they had a child named Day. This made the 'Mischievous One' the grandfather of Night and great-grandfather of Day. To be honest, Loki, Sigyn, and Nari kind of sound like your typical family tale from Norse Mythology. At least until one is introduced to Nari's brother, Váli.
2) Váli – Even less mention is made of Loki and Sigyn's other son, Váli. In fac I have only come across him in the tale of Baldr's Death, historically known as Baldr's Draumar; an amazing tale of magic, death, and torture. The 'TLDR;' version of the story is simple enough: Loki duped some Æsir which resulted in the death of Baldr; Odin and Frigga's son. As it turned out, Odin's family is not to be trifled with and he got very cross with Loki. As a punishment, Váli was magically turned into a wolf that eviscerated his brother, Nari. Nari's intestines were then used to lash Loki down to three large stones beneath the dripping mouth of a venomous serpent. Sigyn stood guard above his head and collected the venom in a bowl but when she had to empty it, the venomous drippings fell upon his face. The writhing from Loki's pain caused earthquakes in Midgard, that's the realm we plebeian humans like to call home.
3) Hel – In ancient Norse culture and mythology, marriage was viewed a little differently than today's standards. It was commonplace for both men and women to marry and take consorts, and sometimes multiple consorts. Loki was no exception and one of his mistresses, Angrboða, a giantess from Járnviðr ('Iron-wood'), bore him three stranger children. We'll kick off Angrboða and Loki's brood with Hel, the, er, least weird one? Hel was actually the Norse Goddess of death and she ruled over the deepest of the nine realms, Niflheimr. What was the off-the-wall thing about this daughter of Loki? She was half living woman and half corpse! This is why the Æsir shunned her to rule over the dead believed to be awaiting reincarnation in Éljúðnir, the hall Hel called home.
4) Jörmungandr – Up until Hel, the half-corpse Goddess of Death, Loki's family was relatively normal, at least for Norse Mythology. Jörmungandr was when things really started to get weird. Jörmungandr was Loki and Angrboða's cute, little serpent son. Yea. Seriously. A serpent. Needless to say, the Æsir were displeased and Thor cast Jörmungandr into the oceans of Midgard, in hopes that it would succumb to a watery grave. Instead of death, Jörmungandr ate all the fish and grew too large for the oceans. After it had fled the oceans, it wrapped itself around Midgard to offer protection from evil and chaos. At least until Jörmungandr took part in Ragnarök. Jörmungandr played a crucial role where it crashed into the oceans and flooded the world as Loki and Fenrir rode Hel's ship upon the waves into the final battle. It was in this last skirmish that Jörmungandr brought an end to all humans in Midgard and to Thor, the true protector of the realm.
5) Fenrir – Among Angrboða's brood was another monster with a myth as epic as that of Baldr's Draumar. Fenrir, the monster beneath the Ván, was Loki's wolf-son. Fenrir was not a werewolf or a shape-shifting human. He was, straight up, a wolf. The Æsir, mainly Odin, felt that he could be tamed so they agreed to keep Fenrir and feed him daily. Being of Jötunn blood, grew into a massive beast of a wolf. He grew so large that only Tyr, the sword-God, was brave enough to continue to feed him. As he grew in size, the Æsir became more and more aware that he would never be tamed and decided he must instead be tethered. So they fired up their forges. Fenrir's strength was so mighty that he busted out of both the chains that the Æsir had made to confine him. Shocked by his might, they called upon the dwarfs of Svartálfaheimr to construct a binding strong enough to hold Fenrir. The dwarf blacksmiths answered the call with Gleipnir, a silken-looking binding that Fenrir was tricked into wearing. Unfortunately, the trick came at the sacrifice of Tyr's sword-hand. As he struggled to free himself, the Æsir managed to jam his mouth open with a sword. The pommel in his lower jaw and the point against the roof of his mouth. The drool the seeped from his agape jaw became the river Ván.
6) Sleipnir – I had to save the weirdest of Loki's children for last and Sleipnir was an easy choice. Loki is the mother to an eight-legged horse named Sleipnir. Yea. You read that right. Mother of an eight-legged horse. Way back when as the Æsir constructed Asgard a wanderer appeared with an offer for him and his horse, Svaðilfari, to construct a wall around Asgard. In return for their work, the wanderer requested the sun, moon, and Freyja, Goddess of love and war. The Æsir thought he could not complete it in time and agreed to this payment but only if it was completed in one year. As time passed, the wall grew around them until there were only days left on the deadline and just a gate to complete. Always quick to blame Loki, the gods and goddesses decided that the wanderer must have been sent to them as a trick; they threatened Loki with a gruesome death should the wanderer finish the wall in time. Loki, motivated by fear, changed himself into a mare and distracted Svaðilfari the only way he knew how. Sex. He had sex with the wanderer's horse. Since Svaðilfari was gettin' busy with Loki-mare, the wanderer failed to meet his deadline. Enraged at his failure, the wanderer revealed himself to be a Jötunn and Thor made quick with the Mjölnir-style smashy-smashy on his skull. It was too late and Loki was pregnant with foal. Some time later, Loki revealed his gray-haired, horse of a son named Sleipnir as a gift to Odin. Sleipnir, with twice the legs as a normal horse, ended up being the fastest horse in all nine realms and found his way into a multitude of other Norse myths.
Well, there you have it. The wild and weird offspring of the mischievous God of fire, Loki. A family lineage wrought with scandal, death, magic, torture, and even a dash of bestiality. Loki's Springer-esque family tale doesn't stop there either. Due to the restrictions of ancient record keeping, we are left with only a few sources for the legends. From not being able to cross reference names, it is actually believed that Angrboða and her son Fenrir got down and dirty to make some incestuous wolf-babes. If this was really how it happened, then not only was Loki a father and a mother but he was also a grandfather-bastard-uncle.