Disclaimer: due to a lack of library access, my resources are kind of limited to old translations, and restricted to England, so I'll leave any relevant evidence from elsewhere in Europe to others.

While it is likely to have happened on occasion, there is not a significant body of evidence that suggests that the Vikings were in the habit of killing women and children. The 12th century Annals of Roger of Hovedon state that in 994, a raid of Sweyn Forkbeard raided in Sussex and Southampton, and "they burned houses, aid waste the fields, and without respoect to sex or age destroyed a very great number of people with fire and sword, and carried off a large amount of spoil; at least, having obtained horses for themselves, furiously raging, they traversed many provinces to and fro, and spared neither the female sex nor yet the innocent age of infants, but, with the ferocity of wild beasts consigned all to death." However, the older Anglo-Saxon Chronicle is less forceful; the same raid is described as "Thence they advanced, and wrought the greatest evil that ever any army could do, in burning and plundering and manslaughter, not only on the sea-coast in Essex, but in Kent and in Sussex and in Hampshire. Next they took horse, and rode as wide as they would, and committed unspeakable evil." This certainly could include killing women and children, I have reason to think that Roger of Hovedon is using this as a justification for an event in 1002 that I will mention below.

The English annals regularly claim that the raiders would commit manslaughter, but apart from this one, I don't know of any references were women are specifically included in slaughters. This absence of explicit evidence is hardly proof that it did not happen, of course, and the slaying of cattle and burning of towns would have led to local hardship, injury, and death, even after the raiders were paid off and long gone. But, it is suggestive that, despite the self-evident bias, they usually can't justify pushing the pagan misdeeds that far.

Certainly, they were taken captive and sold into slavery, at all ranks of society. These slaves were sometimes glorified; the 13th century Laxdaela saga praises the Irish princess Melkorka, who was taken to Iceland as a slave. Slaves would have been very common; while genetic testing has been kind of uncertain exactly how much of the modern Icelandic population is descended from irish slaves (in this case, it would be almost entirely female slaves), Irish people were probably the largest genetic group after people of Scandinavian origin. Ibn Fadlan's account of female slaves in his travels to the 'Rus, while highly stylized, also indicate that capturing women and enslaving them in labor and sexual slavery was fairly common.

Nevertheless, while slavery was fairly common, it was not overwhelmingly so. Even in cases where towns are being regularly burned, people were surviving to offer peace and tribute, including women. And, later English chroniclers were rather envious of the Vikings; John of Wallingford in the 13th century famously wrote that the Danes had been seducing good English women by combing their beards and bathing weekly. While I doubt the difference was that extreme, if their reputation was solidly as indiscriminate murderers, I very much doubt that doing laundry regularly would also clean up their reputation. This is suggestive, at least, that women and children would be spared on raids, especially in favor of non-violent trade or tribute.

So, while all this evidence is suggestive, any violence against women and children perpetrated by the Vikings may not have been regarded as particularly unusual at the time. In 1002, the king of England, Ethelred, ordered the execution of every Dane in England, "because it was told the king, that they would beshrew him of his life, and afterwards all his council, and then have his kingdom without any resistance." Roger of Hovedon again embellishes this story: "[he] ordered all the Danes who lived in England, both great and small, and of either sex, to be slain." I suspect the earlier mention of killing women and children is to justify the brutality of this event, though no link is explicitly drawn between the two events. This event is known as the St. Brice's Day massacre. While it is impossible to say for certain exactly how big this was, mass graves from around the time period have been discovered around Oxford, at St. John's Collegeband at Weymouth Ridgeway, and both have been at least postulated to be related to the massacre. Testing on these indicate that they are almost all young men, and may in fact be raiding parties that were overcome and slaughtered, and not victims of the massacre. Nevertheless, some kind of killing was perpetrated by the English, and may have included women and children.

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The Anglo-Saxon Chronicle, trans. James Ingram, 1823. Accessed at https://avalon.law.yale.edu/subject_menus/angsax.asp.

The Annals of Roger of Hovedon, trans. Henry T Riley, 1853.

Chenery, Caroline, et al. 2014. "A Boat Load of Vikings?" Journal of the North Atlantic, Special Volume X.

Pollard, A.M et al. 2012. "Sprouting like Cockle Amongst the Wheat': The St. Brice's Day Massacre and the Isotopic Analysis of Human Bones from St. John's College, Oxford." Oxford Journal of Archaeology 31, no. 1, 83-102.