“On a slightly different subject... I started comparing the Swedish and English translations of popular songs by the Swedish group Sarek, and noted deep language similarities that perhaps are present in some American regional dialects more than in others. I believe, without a lot of proof or study, that the American south (populated by Scots-Irish, closer to Sweden by the way) has been relatively more strongly influenced by Swedish language.”
Except the Swedes had little to do with the Nordic migration to the British Isles.
It was mainly Danish and Norwegian tribes.
So your premise may be correct if you replace “Swedish” language with “Scandinavian” language.
Historically the Scandinavians had greater influence in the north of Britain and in Ireland.
And of course the French speaking Scandinavians had their impact, as Normans.
The language closest to Olde English is Frisian.
Agreed... Swedish -> Scandinavian.