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.
Denmark ruled Norway from 1319-1814. So a lot of Danish influence remained. The height of Norwegian immigration occured between 1850 and 1880. Danish was still considered the academic language at the time even though the Norwegians flipped the vowels.
Even today the Sognefjord dialect sounds archaic. I was there last summer (my wife was born in Sjolden) and they were difficult to understand even for my wife.
Back then it was even worse as dialects varied from valley to valley as people didn’t travel around much. Still today there are very strong dialects. By watching the news you can tell where people are from almost immediately.
Fortunately, my wife has lived in west Oslo since she was a teenager so she speaks the closest thing to spoken bokmål.