Women are normally assumed to have had control of all domestic activities: food preparation, textile production, laundry, and so on. Their power ended at the house door, while men controlled everything else. Despite this, women were not powerless, as the blog linked from the photo discusses. Women like Auðr djúpúðga (Aud the Deep-minded) could wield a lot of power, and the example of the Oseberg burial shows that some women were deemed powerful enough to have hugely expensive burials.
Women of power
The Oseberg ship burial was the last resting place of two women, at least one of whom was powerful and rich. The range of goods left in the burial mound, even after it had been robbed, bespeaks huge wealth and also gives an indication of the skills and roles that even powerful women had. The burial goods included textile production materials, as well as some surviving textiles, cooking utensils and equipment, spades, hoes, axes and other tools. There were also sleds, a wagon, lamps, a bed, and many other items that shine a light on life in the Viking Age for a powerful woman.
The vast wealth deposited with these women is a demonstration of the power of they were accorded in death, and it is entirely possible that they wielded vast power in life too.
One role of women was that of vǫlva 'cult leader' or 'prophetess'. Vǫlva is one of a range of words used for wise-women or seers. It means wand-carrier and a number of staves or wands have been excavated that might have been carried by a vǫlva. The saga of Eirik the Red includes a sequence where a vǫlva is invited to prophesy and advise for the future.
Women as the conscience of men
The Icelandic sagas often depict women as 'inciters', goading their men to take action. Women do this by presenting a man with the bloody clothes of someone whom they think needs to be avenged, or by speaking harshly to them. Such goading can result in violence where none should be, such as in Laxdæla saga where Bolli is incited to slay his foster-brother Kjartan. In this case Bolli is in a difficult position, because he is meant to take revenge, but the target is his foster-brother which effectively means slaying within his own family, an act that no good Viking would do.
Women and wergild
The Icelandic law code Grágás includes a section called Baugatal that deals with compensation payments for killings. It divides those involved into different levels of responsibility, and, in all bar one case, those responsible are male. The one case is where a fatherless, brotherless, sonless man has been slain (p. 201 in the linked book). In this case, the woman is said to act as a son, adopting a male role and identity for purposes of the claim. To be eligible to do this, she must be an only child and unmarried. As soon as she marries, all responsibilities for pursuing claims are passed to her kinsmen, and her control of the wergild passes to her husband.