Something to note is that elk/wapiti (Cervus canadensis) do not exist in Europe, only moose (Alces alces). This has caused confusion with the word elg between me (from the US) and Norwegians. Using the power of Wikipedia, it looks like one would use wapiti for elk and elg for moose.
Elk is indeed one of the accepted translations of the Norwegian word, "elg."
The Eurasian Elk is (virtually) the same as the North American Moose, (they differ by a very few genes).
The animal that North Americans refer to as an elk (aka "a Wapiti") doesn't exist in Europe, but is referred to as en Wapitihjort.