I am usually skeptical of narratives that put the narrator in a good light, so I presume I was given a very generous retelling of what has come to be known as "the Viking age" when I am from where the vikings originated. In short, we were told of the history in such a manner, that the settling, trading and raiding Vikings were the main contributor to England's success (Via Normandy to English throne), and that of the various Russian countries (grounded a lot in the Rus in Russia, Belarus, Ruthenia referring to Vikings) and traded everywhere from the Asia Minor to the southern coast of Spain and briefly settling in North America. In fact, they were given the same historical importance as the Greek city-states and the Roman empire, which is a level where my bullshit detector goes a little off.
I won't go into how incredibly vague a measure such as 'success' is when comparing empires and peoples from across multiple centuries of time.
Most of what you were taught in terms of the breadth of Viking movement and expansion is however true. The Vikings raided, invaded and settled in many diverse areas during the 8-11th centuries. These included Ireland, England, Scotland, France, and parts of Eastern Europe. Indeed the name 'Russia' stems from the Rus, who seem to have been Scandinavian warriors invited to help settles some disputes in what is now northern Russia, and expanded rapidly over the following centuries.
Also Scandinavian ruins have indeed been found in North America, but note that these were in no way permanent settlements and left no real lasting impact besides their mention in some Icelandic/Greenland sagas.
Also, the claim about the Normans is grounded in historical reality as well. I don't know how much of English 'success' (again an incredibly vague and fought term) was due to the Norman invasion, but the Normans were indeed descended at least partially from vikings who were invited to stay there by the King of France. By the time of their invasion of England in 1066 however, they were far more similar to other continental European cultures than to their sea-roving renegade forefathers.
I will post sources once I've gotten of my phone. Hope this was somewhat helpful.
For a well recorded instance of Scandinavian (should be used instead of Viking - the latter is more of a term specifically used for raiding groups as opposed to traders, invaders or settlers) conflict with another kingdom(s) you should look a the Great Heathen Army's invasion of England (divided at the time into several different sub kingdoms) in the 860s.