In the real world, Denmark and Norway were in a union from 1536 to 1814; but Denmark decided to side with Napoleon in the Napoleonic Wars and was ultimately forced to give Norway up to its arch-rival Sweden. Sweden had a few years before lost Finland to Russia in the Finnish War 1808-09.
In an alternate world, Denmark could have chosen to instead side with the Coalition against Napoleon. Instead, Denmark could have decided to side with Sweden in the Finnish War, preserving Finland for Sweden. The price of this aid may have been a marriage between the Swedish Crown Prince Gustav and the Danish Princess Caroline. This would tie the Scandinavian countries closer together and end the ancient rivalry between Denmark and Sweden, paving the way for a new union of Denmark (including Schleswig and Holstein), Norway (including Iceland and Greenland), and Sweden (including Finland and Pommerania). This union would be a very strong power factor in Europe. It is quite possible that this union would ally with the Netherlands, with which especially Denmark have historically had close ties, though I think real union with the Netherlands would be unlikely.
Since the United States was founded in 1776, it is unlikely that this Scandinavian union would be establish colonies there, but the northern territories of what is now Canada would be another matter. In fact, some French colonies could have been conquered during the Napoleonic Wars if Scandinavia fought against France.
A possible pagan revival is a different matter, which I consider very unlikely. Christianity was very strong in Europe in the 18th and 19th centuries, and if Scandinavia converted to paganism, this would be a strong casus belli, and Scandinavia would likely be divided between Great Britian, Russia, and various German states. Nor is it likely that Viking ships would make a comeback as warships, since clinker-built ships can't be built as large as the carracks that dominated colonial times. Ornamentation inspired by Viking times could make a comeback, though.
An earlier point of departure from history could be the Great Northern War (1700–1721), which was a conflict in which a coalition led by the Tsardom of Russia successfully contested the supremacy of the Swedish Empire in Northern, Central and Eastern Europe. The initial leaders of the anti-Swedish alliance were Peter I of Russia, Frederick IV of Denmark–Norway and Augustus II the Strong of Saxony–Poland–Lithuania.
Sweden had grown very strong under Karl 11, who died young; at age 41 in 1697. He was replaced by his young son, Karl 12, who was just 15 years old. The inexperience of the young king was a major reason for attack by Sweden's opponents.
In an alternate reality, Karl 11 might have lived longer, ensuring greater stability, Karl 11's wife was the Danish princess Ulrikke Eleonore, who also died young, age 36, in 1693. If she had lived on with Karl 11, Denmark would be unlikely to go to war with Sweden - in fact, their marriage was meant to create closer bonds between the two countries. This could mean that the Great Nothern War never happened and that Russia did not gain power in the Baltics. Swedish-Danish relationships might have continued to grow warmer, resulting in a closer union.