It’s going to take several posts to debunk popular misunderstanding about how the pre-Christian Germanic peoples understood the afterlife, to the extent that they believed such a thing existed (as with most things, they conceptualized death differently than we do). Some of that work was already begun in a discussion of the Norns, which you may wish to review, with some additional discussion in a post on Thor’s home Thrudheim.
One of the key misunderstandings is that every Viking expects to go to Valhalla, and you get to Valhalla when a Valkyrie plucks you off the field of battle. This is not accurate.
First, the entire population of northern Europe did not consist of warriors who could be chosen by the Valkyries for Valhalla, whose name means literally “choosers of the fallen”. While many coastal northerners were Viking (raiding) during this time, it wasn’t the only thing they did, and few lived lives of constant battle. It would be foolish for any but an elite few to anticipate living through so much battle that they would be assured a seat in Odin’s mead-hall.
Instead, we must well remember that the Valkyries were agents of Odin, and were in fact extensions of his consciousness. They chose those for Valhalla who Odin preferred to be among his einherjer. His first priorities include the sovereign class, such as kings, jarls, and other nobles. Then those who go through specific rituals to enter shamanic battle trances, such as berserkers and ulfhethnar, who transformed themselves into an animal rage on the battlefield. If any warriors had a special relationship with Odin, or were members of the Odin cult, they, too, had the promise of Valhalla.
Of course, Odin was selecting men (and possibly shield maidens) for the einherjar to stand against Loki and a slew of monsters and dishonored dead at Ragnarök. As the supreme sovereign, he had the right to reject any of those who might have been less-than-able fighters in the final battle, and he could use his Valkyries to choose any warrior of exceptional valor.
Once they arrived in Valhalla, the einherjar battled one another in training from dawn until dusk to practice for Ragnarök. Any warriors who fell during battle were resurrected the next day to battle again. In the evenings, there were great feasts and drinking in honor of Odin and in memory of many great battles.
Fallen warriors who are not chosen by the Valkyries are taken by Frejya to her blessed land of Folkvang, which is in no way a punishment or dishonor.
It is worth noting here that neither Valhalla nor Folkvang are mentioned in the sources as being part of Asgard. They are more likely part of Hel, the realm of the dead.
So if Valkyries are agents of Odin, and perhaps even extensions of his self, how are they described?
In one poem, reference is made to a Valkyrie having a particularly fair face. In another, they are mentioned wearing helmets, with mail armor covered in blood, with a shield or with bright light shining from their spears. Some lists of Valkyries give some description of what they looked like and how they behaved from the translations of their names: Skuld (“debt”), Skögul (“shaker”), Gunnr (“war”), Hildr (“battle”), Göndul (“wand-wielder”), Geirskögul (“Spear-shaker”); Hrist (“shaker”) and Mist (“cloud”), Skeggjöld (“axe-age”), Thrudr (“power”), Hlökk (“noise” or “battle”), Herfjötur (“host-fetter”), Göll (“tumult”), Geirahöth (“spear-fight”), Randgrith (“shield-truce), Radgrith (“council-truce”), and Reginleif (“power-truce”) (I’m grabbing these name translations from Wikipedia, but I know several to be accurate without looking to better sources, so..forgive me?). With only a few exceptions, these are the names of war and battle, not the names typically associated with femininity. And their deeds in stories where they are not merely serving Odin involve battle, fighting side-by-side with men, and spurning men romantically – these are women far different than even the goddesses who have been passed down to us, who are hardly mentioned (Sif) and mostly passive (Idunn).
This militaristic shade to the Valkyries aids in another shading to the meaning of the phrase “choosers of the fallen”, as they also decide during the battle who will die. They are also enacting Odin’s sovereign function here, as he has a divine interest in the winner of each battle, as a matter of acquiring warriors to join the einherjar, so that the outcome might better serve his true goal, avoiding Ragnarök, and for any other earthly or divine purpose he might have. The Valkyries are Odin’s agents on many levels.
In their association with death and battle, they are very closely associated with Odin. But some depictions also show them as bearing some resemblance to the Norns, specifically referring to the Valkyries gathered alongside the battlefield, weaving the results into being, but with grisly tools – intestines instead of yarn, skulls instead of bobs, bones for needles, and so on. And there is some confusion over just how closely Freyja was associated with the Valkyries – was she simply the chooser of a different class of fallen, were the Valkyries patterned after her, or was there some symbiotic relationship between the two? Given that some insist Freyja was synonymous with Frigga, wife of Odin, there may have been a great deal of overlap, and the Valkyries could have been Freyja’s warrior-women as much as Odin’s.
As with all things related to the pre-Christian Germanic conception of the dead, the Valkyries are complex beings. They appear to be working Odin’s will on the battlefield, both during the battle and to manage Odin’s chosen as they fall. But they seem to have their own lives as well, sometimes living away from the battlefield for years at a time. They are neither wholly Odin’s nor wholly their own. Perhaps the metaphor says something of everyone’s connection to the greater universe, and refers back to the greater feminine influence on caring for the dead and for destiny in general.
In any case, they are not angels sent from heaven to lead Vikings off to their happy reward. They are vicious, have an agenda that is not beneficent, and choose perhaps half the battle-slain, who are themselves but a small percentage of all who died during the Viking Age. They are only a small part of the Viking (and broader pre-Christian Germanic) conception of death and the afterlife.