[they spoke an archaic version of his language]
It’s called Danish...most who emigrated were still under Danish rule at the time and spoke it.
I think you mean Sweden? The Danes were replaced by the Swedes around 1814. The settlers here date from the 1880s.
No, they actually speak an 18th-19th century dialect of Norwegian. Most of the Westby Norwegians came from Sognafjord. Some emigrated from Trondheim. From what the modern Norwegian speakers say, it is analogous to listening to Chaucerian English while being a 21st century Brit. I gather that even back then, there was already a linguistic divergence between the rural farmers/fishermen/peddlers and the city folk from Oslo.