Conversion of Scandinavia
Unfortunately the sources for the conversion of Scandinavia are (as always) few, unreliable and contradictory.
However, it is possible to give a "potted history" of the likely sequence of events that is hopefully not too inaccurate.
Early Missions
Saint Willibrord
Alcuin's life of Willibrord tells us that in the early eighth century he visited a Danish king called Ongendus. Denmark was not a unified kingdom at the time, and the extent (if any) of Ongendus' hegemony is unclear, though the existence of the Danevirke is held by archaeologists to demonstrate that there must have been a powerful overlordship of some kind. Willibrord is said to have taken thirty boys away to train as missionaries and send back, but we are not told the ultimate outcome and other sources do not suggest that an effective mission followed. It suffices to note that following a single visit to one of multiple kings, Willibrord became better known for his other work as "Apostle of the Frisians".
Saint Anskar and friends
The two key texts for missionary efforts from northern Germany are Rimbert's Vita Anskarii (Life of Anskar) and Adam of Bremen's Gesta Hammaburgensis ecclesiae pontificum (Doings of the Bishops of the church of Hamburg).
Without delving too deeply into ecclesiastical politics the purpose of these texts was to promote the German bishopric of Hamburg-Bremen, and emphasise its role in the conversion of Scandinavia. They were successful in this, Hamburg-Bremen became the Archbishopric for Scandinavia and accrued power and influence, and generations of historians accepted the accounts at face value.
Adam of Bremem tells us that Anskar baptised one Harold, king of the Danes, and with Autbert "spent two years in the kingdom of the Danes and converted many of the heathen to the Christian faith." Later, it is written that he
"and Witmar sailed across to Sweden where they were kindly received by King Bjorn and were permitted publicly to preach the Word of God. And so in the course of one year they won many to the Lord Jesus Christ, among them the prefect of the town of Bjorko, Herigar, who, they say, was himself distinguished for his miracles and wonder-working powers."
And it is claimed that in 831 Hamburg was appointed "as the metropolitan see for all the barbarous nations of the Danes, the Swedes and likewise the Slavs and the other peoples living round about. And he had Ansgar consecrated as the first archbishop of this see."
Anskar's successors too are held up as successful missionaries: "Rimbert ... actively discharged ... the duty of preaching the word of God to the heathen ... He, indeed, personally pressed this mission vigorously as often as his other work permitted."
"Adalgar received ... his pontificate ... in a hard time of barbarian devastation. Nevertheless he did not, as is evident in the privileges, yield in his endeavour for his mission to the heathen"
However, there does not seem to have been enduring or wide-scale change as a result, with Adam admitting that by the episcopate of Hoger in the first two decdes of the tenth century, "they were all pagans and that there was little of the Christianity which Ansgar had planted and which did not entirely disappear."
The Tenth Century - Denmark and Sweden
Harald Bluetooth
In about 960, Harald Bluetooth came to rule Denmark. While his father, Gorm the Old, had (according to Adam of Bremen) set about completely to destroy Christianity in Denmark, Harald was militantly Christian - in a literal sense, and against their will [he] compelled [the Danes] to embrace Christianity.
The view of Harald as convertor of Denmark is enshrined in the Jelling monument, where runestones show Christ in glory and state that King Harald had this memorial made for Gorm his father and Thyri his mother: that Harald who won for himself all Denmark and Norway, and made the Danes Christian.
Svein Forkbeard
Harald's heavy handedness, we are told, led to an anti-Christian rebellion to put Harald's son Svein on the throne, backed by the Swedish king Eric - who then took power for himself. Svein, however, then found God, and empowered by his new faith succeeded to throne when Eric promptly died - Eric's son Olaf was a good christian and returned it to him.
However true this version of events is, it serves to show the vulnerability of the new conversion, though by the end of Svein's reign it seems to have been firmly established.
Viking armies owing allegiance to Svein, especially towards the end of his reign, and those loyal to his son Canute, should not be anti-Christian and should not be given to overwhelming outwardly pagan practices.
Olaf Ericsson
Meanwhile in Sweden, Adam tells us, Olaf made Harald-like efforts to oppress paganism, trying to destroy temples and idols. The Swedes, however, were having none of this, and while they did not depose him it was agreed that he would not force anyone to become Christian, and would only proselytise in certain areas. This may be an exaggeration, given the agenda of promoting Hamburg-Bremen's influence and the supposedly strong support that Olaf gave to the see despite his limited ability to do so.
It's worth noting that although Adam says Olaf was converted by Poppo of Hamburg-Bremen, this is also recorded as the achievement of English missionaries in Västergötland. However, it's clear that whoever is due credit Olaf was certainly converted by someone. Adam acknowledges the presence of English missions, noting how a certain Englishman named Wolfred, inspired by divine love, entered Sweden and with great courage preached the Word of God to the pagans - though he was killed for anathematising Thor, so clearly Christianity's position was still fragile.
The Tenth Century - Norway
Hákon Aðalstansfostri
Hákon Haraldsson, son of Harald Hárfagre, known as "the Good" was fostered by Aðelstan and thus spent his formative years living in a Christian court. Having driven out Erik Bloodaxe to claim the Norwegian throne in 934, he does not seem to have attempted to impose Christianity from the top down. Although Heimskringla tells us that "many, out of friendship to him, allowed themselves to be baptised", Hákon seems to have been forced into pagan observances by his subjects, in order to keep his throne.
Although not bringing about mass change, Hákon is notable as a Christianising influence with roots not in Germany, but Anglo-Saxon England.
Following Hákon Aðalstansfostri's rule, Norwegian rulers did not actively pursue Christianity for some time. Most notably, during the second half of the tenth century Norway was ruled by Hákon Jarl, a conservative figure who did not call himself king and was vehemently anti Christian/pro-pagan. Norwegians at events set between 975 and 995 may wish to emphasise their non-Christianity in a "last hurrah" before the country's conversion.
Olaf Trygvasson
Following the firmly pagan Hákon Jarl, who had resisted attempts by his politically powerful neighbour Harald Bluetooth to convert him, Olaf Trygvasson came to rule Norway. Most of the sources offering any sort of detail about him are rather late, but his reign (995-1000) seems to have seen a rapid and firm imposition of Christianity on Norway through centralised use of force.
Olaf issued coins bearing the sign of the cross copied from those of Aeðelraed, suggesting English influences during his reign.
From Olaf's reign onwards, royal armies from both Denmark and Norway should be predominately Christian in character with Paganism limited to quiet private practice at best.
The eleventh century - Canute and Saint Olaf
From 1014 Canute (the second king of England to be known as "the Great") ruled both England and Denmark, and later ruled Norway too.
Although from Denmark, Canute ruled England using existing, English structures, and was a strong Christian monarch who patronised the church. Archbishop Wulfstan of York prepared law codes for him that were similar to those of his native predecessors, and he is pictured in the well known frontispiece to the Liber Vitae of New Minster Winchester together with his wife donating a crucifx to the church.
The much-mis-used story of Canute trying to turn back the sea is not about his vanity, but his demonstrating that the most powerful of kings cannot countermand what God has put in motion.
When Canute took the throne of Norway, it was from another Christian, Olaf Haraldsson. Olaf had brought Grimkell, an English Bishop, to help Christianise Norway, and has traditionally been seen as a significant christianising influence. Following his death at the battle of Stiklestade, Olaf was venerated as a saint by his disposers, helping to further strengthen Christianity in Norway.
From Canute's reign onwards, Scandinavians in England should be predominently Christian and outward signs of paganism are discouraged.
While the conversion of Sweden lagged behind, with Blot Sweyn an uncompromising pagan king as late as the 1080s, any Swedes well enough travelled to be visiting Britain would be familiar with Christianity and keep their religion quiet unless looking for trouble. This can provide an interesting acting opportunity, but should not be taken as a license for great numbers or significant shows of paganism, and should be supported by appropriately Swedish kit.