There is quite a lot to be said about this topic. I'm not sure I'm the best person to give a full answer to your question, since this is a topic on which entire books could be based, but I'll at least try to give an answer regarding the connections between Norwegian and English language.
The first major language influence between the two languages started with the Viking raids from around 800 B.C. The Vikings didn't just pillage and plunder in the British Islands, they also settled in certain areas, and for several centuries large parts of England was governed by Scandinavians. The Viking population interacted with the Anglo-Saxons allready inhabiting the area through trade, marriage and other channels, and eventually their languages would blend together. This "bastard language" has been part of the roots of modern English, and you'll therefore find quite a few words in the English language that stem from ancient Norse words, particularly within the dialects in Yorkshire and other northern areas in England.
Today the influence is solely in the other direction. Since the days of the British Empire, English has become a world language, and both English and American culture and language has for centuries been ever more influential in Norway, much like it has all over the world.