Norway was still unified with Denmark at the time of the conversion (and for centuries after). Even going so far as demoting Norway from a kingdom to a province in 1536.

So, because of this, the conversion of Denmark comes first. Frederick I was King of Denmark and Norway when much of the population of Denmark was converted to Lutheranism. He, himself, never converted but was fairly sympathetic (or, at least, apathetic) to the Lutheran religion. Unlike Catholic counterparts elsewhere on the continent, he didn't suppress the spread of Protestantism within Denmark. And he even went so far as closing some monasteries and taking bishop appointments away from the Church (although he still remained Catholic). So a good portion, although hardly all of it, of the country had converted by the time of his death. Although much of the nobility had not. His son, Christian III, was deeply Lutheran. He had heard Martin Luther speak and had a very personal connection to the religion. So he took it a step further and made Protestantism, of the Lutheran persuasion, the official religion of both Denmark and Norway in 1537. His religious practices were known before his succession and he faced a war over his succession by Catholic adversaries (both at home and abroad). He was successful but it wasn't an easy win. There was an attempt at opposition within Norway but that didn't have much traction. Largely because of how lightly populated it was and how dispersed that population was.

So, by 1536 into 1537 the official religion of Denmark and Norway was Lutheranism.

Norway was less populated than Denmark but they were pretty devoutly Catholic as much as they were anything. There were definitely a number of villages in Norway that didn't have a regular weekly priest. So, there may have been a number of people who didn't feel the strong attachment to the Catholic service. Attachment to the service and the rituals of the Catholic Church had been a major impediment to conversion elsewhere (such as England). But, on the other hand, they also didn't have any particular resentment toward the Catholic Church that might be found elsewhere. They weren't witnessing much corruption within the clergy that Martin Luther spoke out against. At least, not on a massive scale. The Church in Norway would have been too small and poor for that. (Although much of that corruption was happening higher up than the parish level in every country which was why conversion was so often a top down thing.) Not that Church corruption was the only factor, or the most important, in conversion or the Protestant Reformation. But it was often an easier factor to get people worked up about than some doctrinal issues. The other issue that tended to motivate people was the ability to read the bible and speak to God without an intermediary but this was often more true of the merchant class (people who could read but wouldn't necessarily learn Latin.) Norway didn't have a large merchant class either. There were literate farmers, of course, who were crucial in witnessing local transactions and contracts. But much of the population wasn't literate. (And there was a shift where Danish became the official language and, thus, the official written language which would have alienated even some of the moderately literate people.)

So, conversion was slow and plodding. There wasn't the large scale resistance found in other countries. But it also was not an immediate embrace. The official adoption of Christian III didn't have much immediate impact, he couldn't really force it on Norway in a practical way. He did confiscate Church land (which was a significant percent of land in Norway) and get rid of the religious orders. But that wouldn't have much impact on what was being preached in the village churches. Norway also didn't have a major university for Lutheran preachers to train at and disperse the message. So, Lutheran preachers would emigrate to Norway from Denmark and travel through out. That took time. So, over time the people were converted. It's difficult to gauge how long it took. Because it was such a decentralized state. But it definitely wasn't one large conversion.

So, long story short, it spread to Norway because Christian III of Denmark demanded that it must. Even then it took some time. There weren't any political consequences because that's what their sovereign wanted. I can't speak to the social consequences.