Skrälingborg (Skrælingborg), 1648
After the Peace of Brömsebro in 1645, Skrælige became a Swedish possession. Sweden already controlled land on the North American continent, an area known as Nya Sverige since 1638 (New Sweden - centered around present day Wilmington, DE, USA). Given the distance between Fort Christina and Skrælingborg, Skrælige was setup as its own self-governing colony, Skrälig Öar.
Once the appointed Swedish governor arrived, a couple of significant changes happened. First of all, the trade monopoly was loosened - while trade with Sweden (incl. New Sweden) was preferred, trade with New England and New Netherlands was now legal. This change did a lot to put the Swedish government in the people's good graces - the new government was finally doing something that benefitted Skrælige, and was not solely to the benefit of Sweden.
Second, a truce was made with the Abenaki. This was mostly a strategic decision on the part of Sweden: Skrælige was isolated from New Sweden, and was surrounded by other great powers. While the Abenaki were not a major threat, unnecessary aggression towards them would tie up military resources that might be needed elsewhere. The Abenaki were of course weary of the Skræligen government, but were glad to no longer be the focus of constant aggression.
Governor's Residence, Skrälingborg, 1648
Nördställe (Norðstaðr), 1648
With Skrælige changing hands multiple times over the last century, the population of the small settlement was becoming a bit more diverse. Back when Skrælige was originally settled, the population was mainly Norse-speaking immigrants, with some integration with Abenaki people. In the 16th century there was some trade with the Spanish (Castilian) colonies to the south. This did lead to a couple of Spanish merchants settling in Skrælingborg for extended stints, but there was no significant demographic shift. This changed in the 17th century, with immigration now coming from Denmark (as well as Norway, which was ruled by the same monarch, and Iceland). With Swedish rule, Swedes and Finns (who were currently ruled by Sweden) immigrated as well. In addition, a small number of English people left the Puritan New England colonies to settle in Skrælige instead, but this was a fairly minor source of immigration.
After the immediate acts of the Swedish governor, work soon began on another census, this time called the Folkräkning. There were some delays as Sweden was still involved in the Thirty Years' War, but this was completed by 1648. The results were as follows:
Skrälingborg (Skrælingborg): 800 (+328)
Church & Market District: 361 (+189)
Mittensätt & Nya Hamnen (Formerly Midtvej/Miðrway & Nyhavn/Nyjahofn): 373 (+136)
Outside of the walls: 52 (+3)
Vänsterväg (formerly Venstrevej/Vinstrileið) village: 14 (-)
Mittentunga (formerly Midtunge/Miðrtunga): 98 (+56)
Nördställe (formerly Nordsted/Norðstaðr): 218 (+151)
Kopparsten (formerly Eirsten/Eirsteinn): 71 (+16)
Nyhoppas (formerly Nyhåber/Nyrvænn): 184 (+34)
Main Village: 161 (+34)
North Village: 11 (+1)
South Village: 12 (-1)
Abenakiborg: 9 (-1)
Karlsborg (formerly Christianborg): 128 Soldiers
Litenvik (formerly Lillebugt/Smarvik): 73 (+38)
Rasböja (formerly Rasbøje/Rasbeygja): 16 (+16, formerly abandoned)
Mittensunborg (formerly Midtsunborg/Miðrsunborg): 37 (+16)
Egilställe (formerly Egilsted): 35
Total population of 1669 (+823)
The count also included 27 slaves. 145 of the Skræligens were recent immigrants from Sweden and Finland. The Danish and Old Skræligen* populations were substantially mixed by this point, with a Skræligen-speaking majority and a substantial Danish-speaking minority. (These refer to their native languages - there was a degree of mutual intelligibility, and many were bilingual.)
*Descended from pre-Isolation Skræligens
Meanwhile in Europe, a war known as either the "Second Northern War" or the "First Northern War", started in 1655. The conflict primarily began as a Swedish invasion of Poland-Lithuania, but expanded to include Brandenburg-Prussia, the Habsburg Monarchy, Russia, Denmark-Norway, the Dutch Republic, and others.
New Sweden was settled on land that was also claimed by the Dutch, and so this war presented an opportunity to invade New Sweden. In the summer of 1655, Director-General Peter Stuyvesant of New Netherland led most of the colonial garrison to the Delaware River. They recaptured Fort Trinity* on the 11th of September, and besieged the capital Fort Christina. New Sweden surrendered on the 15th of September, but was able to maintain significant autonomy under the Dutch.
Stuyvesant also had plans to invade Skrælige - Dutch claims extended further east than the settled areas of the Hudson Valley, and Skrælige would be a strategic position to occupy. This was planned to come after the invasion of New Sweden, but a new war broke out the very same day of Sweden's surrender - the Peach Tree War. The Susquehannock people were already distrustful of the Dutch due to their alliance with the Iroquois Confederacy (an enemy of the Susquehannocks). On the 15th of September, around 600 Susquehannock warriors landed in New Amsterdam, which was very lightly defended due to the invasion of New Sweden. Several outlying villages were destroyed, and hundreds of hostages taken and ransomed. (The death toll is unknown.)
After this attack, some of the outlying towns were permanently abandoned, and the ones that were resettled were to be heavily fortified. Invasion plans for Skrælige had to be put on hold to carry out this work.
*Fort Trinity was originally settled by the Dutch in 1651, named Fort Casimir for the Polish king. It was conquered by New Sweden in May 1654 and renamed Fort Trinity.
New Sweden & New Netherland c. 1650
In the midst of the conflict to the southwest, the Colony of Massachusetts Bay saw an opportunity for expansion. Skrælige was arguably within the charter area of the colony, and in the spring of 1656 colonists settled the village of Northney on the northernmost island of Skrælige, what was known as Norþæn in Skræligen. Due to the war on the continent, the Swedish government in Skrälingborg did not try to capture the settlement, as doing so might antagonise the English. As long as the English stayed on their island, the government was content to allow them to remain.
Karlsborg under Swedish control, 1657
By the summer of 1657, New Netherland had sufficiently recovered from the Peach Tree War enough to plan its invasion of Skrælige. This was a controversial decision, given Skrælige's distance from New Amsterdam and the consequences of the last invasion. However, the war in Europe was still going, and the Dutch government saw Swedish Skrælige as an important strategic objective. Not only would taking the islands remove a potential Swedish threat, but it would also be a thorn in the side of New England. The English and Dutch previously had competing claims in the Connecticut River Valley (then also known as the Fresh River), and had taken over Fort Goede Hoop (present day Hartford, CT) in 1653, so a fortification on the other side of New England could put them in a better position.
Director-General Stuyvesant sent a squadron of ships to the islands, landing a force at Rasböja and then sieging Litenvik (Smarvik) from both sides on the 3rd of August, 1657. Given the vast firepower discrepancy between the small settlement and the Dutch force, Litenvik surrendered without a fight. With the southern end of Storreyn under control, the Dutch forces moved north, blockading Skrælingborg from the west and south, and putting Karlsborg (formerly Christianborg) under siege. After putting up a fight, the lack of any reinforcements meant that continuing to fight would just postpone the inevitable. And so on the 9th of August, 1657, Skrælige became part of Nieuw Nederland.
Overhead view of Skrælige c. 1660. Skraalingborg (Skrælingborg) in the centre to the south of the Siguan River, Noordstaadt (Norðstaðr) to the north, Willemfort & Nieuwehoop (Nyrvænn) to the southwest, and Middentong (Miðrtunga) to the east.
Noordstaadt (Norðstaðr) c. 1660
Linker Weg, Skraalingborg c. 1660
Governor's Residence c. 1660
With the Dutch invasion, Skrælige was now controlled by New Amsterdam. Now known as Nederlands Skraalig Eilanden, the region was given quite a bit of autonomy. The Skræligen Þing had existed under Danish and Swedish occupation as an advisory body, but was now given formal authority of the islands - still under the ultimate control of Director-General Stuyvesant though.
Although no full census would be taken during this time, the official names of some settlements were renamed as follows:
Skrälingborg was renamed Skraalingborg
Mittentunga became Middentong
Nördställe became Noordstaadt
Kopparsten became Kopersteen
Nyhoppas became Nieuwehoop
Rasböja became Raskromming
Mittensunborg became Middensunfort
Egilställe became Egilstadt
Karlsborg became Willemfort
While the truce between the Skræligens and the Abenaki continued during this time, there was no such truce with the Northney settlement. The English settlers up north attempted to expand across the channel onto Storreyn itself. This would have been a much more significant violation of Dutch land claims - they were willing to put up with an incursion onto a mostly uninhabited island, but reaching the main island would be difficult to ignore. However, by this point in time the Abenaki were armed with muskets, and English attempts to cross over were easily repelled.
Throughout the 17th century there was a significant commercial and maritime rivalry between England and the Dutch Republic, which led to frequent conflict. Even when the two countries were at peace, their trade companies had their own warships and were in conflict. Among other grievances were the English Navigation Acts, which required all trade with English ports (including the colonies) to be done with English ships. The First Anglo-Dutch war broke out between the Commonwealth of England and the Dutch Republic between 1652 and 54, and while England won the war, the commercial rivalry was entirely unresolved.
With this context, the English were agitating for another war, including capturing the Dutch trading outpost on Cabo Verde in late 1663. Subsequently King Charles II granted his brother James (later King James II) the land from the Delaware River to the Connecticut River - land which included New Netherland. In May of 1664 Colonel Nicolls set out from Portsmouth, England, and after enlisting the support of English militias on Long Island, arrived at New Amsterdam on the 4th of September. Nicolls had proposed a fairly lenient surrender agreement, including continuation of property rights and freedom of religion, in order to encourage a peaceful surrender. While Peter Stuyvesant was initially inclined to resist this, the burghers and his son met with him to force him to concede, and the Articles of Surrender of New Netherland were signed on the 6th of September.
The English sent troops up the Hudson River, and Fort Orange promptly surrendered on the 24th of September, to be renamed Fort Albany. Former New Sweden was captured in October, and then on the 24th of October a squadron of ships arrived outside Willemfort in Skrælige. Given the same terms as New Amsterdam, the Dutch garrison promptly surrendered, and Skrælige (apart from Northney) was to be part of the Province of New York.
The lines on the "European Colonisation Around Skrælige" map are... kind of made up? There's a few different sources I used (listed below).
One source was a map of towns in New England c. 1700 (i.e. from the future): https://commons.wikimedia.org/wiki/File:New_England_Town_Lines_and_Borders_in_1700.png. I interpreted the presence of an incorporated town to mean it was probably actually controlled by the colony, and not just claimed. The outer borders of CT & MA are their modern ones - the border areas weren't really controlled by anyone anyway, and there were plenty of conflicting claims, even between English colonies.
For the MA/CT border, I went with the 1700 one - there was a 1642 MA survey line, but again there was no actual colonial control so it didn't seem right to make a definitive line of control.
NH/CT divide is based off of https://commons.wikimedia.org/wiki/File:Ctcolony.png, and I drew my own lines around settlements on Long Island.
One slight error is that Stonington in the southeastern corner of CT was briefly controlled by Mass. Bay right around 1660, but I opted to just not include that since it switches back to CT so soon.
New Netherland & New Sweden use this map: https://en.wikipedia.org/wiki/File:Nieuw_Nederland_and_Nya_Sverige.svg. Obviously those lines are rough estimates and are not borders in the modern sense.