In the late nineteenth and early twentieth centuries, Ibsen's plays seem to have been regarded as very influential, both by people who agreed with him and those who didn't. For example, Oswald Spengler mentions him as one who will still be quoted a hundred years later, as having a similar influence to Marx or Darwin. And Kipling makes "Tomlinson" mention Ibsen as someone that might win him points for getting into Heaven:
Then Tomlinson looked back and forth, and little good it bore,
For the Darkness stayed at his shoulder-blade and Heaven's Gate before:
"O this I have felt, and this I have guessed, and this I have heard men say,
And this they wrote that another man wrote of a carl in Norroway."
At any rate it's hard to see what other Norwegian Tomlinson could possibly mean; Kipling, of course, does not intend this as a compliment to either Ibsen or Tomlinson.
Ibsen is still studied in Norwegian schools, and I've seen "Enemy of the People" performed in English; but I think he would no longer rank quite as high as Marx or Darwin for influence. So what led Spengler to consider him as such? How did a playwright working in the rather obscure language of a small, poor country become so well-known far outside the borders of Norway?
And, bonus question: Having become so famous, what led to the decline of his influence?
I can't adress all of your questions - I'm not familiar enough with the spectific norwegian context of Ibsen's writings, nor with his reception in many european countries (including England). What I can speak of, however, is the reception of his work in France specifically, and I think some of it could be generalized to the european context as a whole, since the emergence of naturalism and of the "mise en scène" are a shifts commons to the whole continent. This reply will be in two parts : 1) why Ibsen's dramaturgy was such a paradigm shift to XIXth-century audiences, explaining the wide reach of his writings 2) why this influence endured for so long
The first play by Ibsen performed on the french stage was *Ghosts*, in 1890, which is somewhat later than in other european countries, notably Germany or England. At the time, theatre was largelly dominated by very commercial productions, with spectacular effects (like faery plays), comedies which were very formulaic, and a general aesthetic still under the influence of romanticism. However, for several decades, some artists had been looking to reform the stage, and most notably to adapt the principal of naturalism to the stage.
Chief among them was the novelist Emile Zola. The theory underpining his writing was that the *milieu* (the social conditions, mainly) explained the actions of the characters. He saw writing as a form of scientific endavour (quoting, for exemple, one of the fathers of the scientific method, Claude Bernard). If you document your "milieu" well enough (Zola made numerous fields trips to make sure of that), then the action of your novel should mecanically follow and represent the social forces at work. It was a sort of sociological vision of litterature. And for a few decades, Zola had sought to share this vision with the theatre, which as the time was the most important media. Some of his novels had been adaptated into plays ; trouble was, they were written by popular authors of the time, who didn't get what Zola was trying to accomplish and turned his novels into the kind of play popular at the time, with a lot of plot twists, some love stories, some devious vilains, etc.
So the "avant-garde" were still looking for ways to make naturalist theatre, but did not have the plays they wanted to do that. So when they discovered Ibsen's writings, it was kind of a revelation : he was very good at creating the "milieu", emphasasing the little details rather than inventing a ton of plot twists, creating characters that seemed to be moved by strong social currents, rather than their individual whims. After the introduction of Ibsen in 1890, he was a huge success in the avant-garde : about 13 of his plays were produced in the next 10 years.
It is no coincidence that the man who brought Ibsen to the french stage, André Antoine, was both an avid follower of Zola and one the the pioneer of the "mise en scène" that was emerging at the time. Plays like those of Ibsen need a director in ways that previous plays didn't, since so much of the meaning rest on the "milieu", on the details, that have to appear significant ; it is a perfect text for someone who wants the stage to give meaning to the text (which is what modern staging is all about). To note, at least an other pioneer of the european mise en scène, Stanislaksi, also staged Ibsen's plays. Moreover, in France, Ibsen was not only successful with naturalist stage directors like Antoine, but also with those which at first glance seem like their polar opposites : symbolists. In the 1890s, Lugné-Poë, the director of the symbolist avant-garde, also staged Ibsen. Symbolist were interested by the ideas, by what could not be physically represented ; and here again, Ibsen's plays were perfect for the job, because of their emphasis on undecurrents. So two really distinct aesthetics were interested in Ibsen for kind of the same reasons, for the way the plays were suggesting things instead of saying them, and they produced two radically different ways of staging Ibsen. Thus, Ibsen's success at the time is at least in part due to the emergence of modern staging : modern staging neeeded modern plays to go with it.
Some specialist, like Jean-Pierre Sarrazac, have shown that there has been a massive shift in the way we write drama since the end of the XIXth century, and that Ibsen/Strinberg/tchekhov really invented a new form of drama, still influencial to this day. To summarize : before, theatre was mostly written according to the aristotelician model : a play was an interpersonal action in the present, with character that were individual, well-defined figures. After that, all those notions - plot, characters, the idea that the action happens in the present etc. - became more and more complicated. This, according to Sarrazac, was Ibsen's invention. At first glance his dramas seem quite classical ; but if you look closely you'll remark that what was the core of previous drama - the plot advancing in the present - is mostly missing because *everything happened before the first scene*. A lot of Ibsen play are just a present in which the past resurface ; the characters are haunted more than they're actors of their life. For people like Sarrazac, this is the reason Ibsen should be considered like (one of) the inventor of modern drama that spanned the whole XXth century.
So, according to this reading, we could hypothesis that Ibsen's plays were so successful because they perfectly fit the modern paradigm of drama that artists and audiences had come to expect.
I would also hypothesis that, during the XXth century, (in France at least), power within the theatre came to rest more on more in the hand of stage directors. As I said previoulsy, Ibsen plays were kind of popular for stage directors since they allowed them to showcase their art ; so this could in part explain was Ibsen was staged often.
I don't think Ibsen's position within theatre declined significantly ; it is rather theatre position in society, as a media, that took a huge hit. If you open any generalist french newspaper of the late XIXth century, you could have about 1/4 of pages dedicated to theatre : reviews, gossip, announcements... It is impossible to imagine today. In the middle of the XIXth century, the average french family spend 87% of their entertainment budget on theatre. Theatre was really the media of the ages. So a person proeminent in the theatre field could be considered as the equal to Marx, because theatre was so important as a media.
This, of course, radically changed in the XXth. The position occupied by theatre was overtaken by the television, and, more recently, the internet. It is now a kind of niche entertainment. So mecanically, someone important in theatre is less important to society as a whole.