As could be expected, idiomatic and grammatical changes have taken place in the Icelandic language spoken by Western Icelanders. Their move to a new world brought the need to create new words. Western Icelanders often used English words to express themselves. This often led to misunderstandings. For example, in Icelandic, the words for "man" sounds very similar to the English word for "call". A joke about a Western Icelandic woman staying in a hotel in Reykjavik illustrates such potential confusion. She asked the staff to send up a "call" This word pronounced with an Icelandic accent sounds like the Icelandic for "man". The hotel workers were perplexed and didn't realize that she had meant to say "give me a wake-up call".
Here are some other examples of anglicized Icelandic. The Icelandic diphthong "ei" is pronounced like "a" in "bay".

Haraldur Bessason, a former University rector in Akureyri, wrote two amusing articles about this subject in Lesbók Morgunblađsins, on 16 and 24 June, 1984. "Ađ rósta upp kjötiđ og klína upp húsiđ"; and "Hún fór út međ bojfrendinu."

"Mixture of languages."
From an interview with Kristin Oddsson in Vancouver.
From interviews collected by Hallfređur Örn Eiríksson and Olga María Franzdóttir among Western Icelanders in Canada and the United States (the Árni Magnússon Institute 1972-1973).

"Icelandic in the West"
From the radio episode The Secret of the Vínarterta (Viennese Torte).
A series of Icelandic National Radio Broadcasts by Jón Karl Helgason (RÚV 1996).