From: Piotr Gasiorowski

what do you mean when you say your father "has [a]"?). The surviving rounded vowel in fork or north will no doubt be analysed as a monophthongal pre-r allophone of the vowel of goat in all accents.

Well, it's the vowel closest to what I apprehend it to be at the Ladefoged site:

His name is Lawrence. My mother, I, and my five siblings all do it more or less as Americans do Olivier's, with the first syllable a (rhotic) homophone of 'lore'. The vowel my dad uses is a little funny. It's not the one in 'law'. It's not the baw-bab-Bob cot/caught vowel. And the R comes out funny because of what you have to do to make that a (there is a 'tenseness' in the throat). 

A Minnesota accent is what you hear in the movie Fargo. This is not really a 'Norwegian accent'. My father does not have the 'sing-song' tonal quality usually associated with it. It's fair, tho', to say there is some sort of Norwegian substratum to his 'accent'.

It's not uncommon in American English to unround the starting point of [oʊ] (the most accurate transcription would be [ɤʊ]).

I take your word for it, Piotr. I listened at the Ladefoged site. [ɤ] ('ram's head', as I remember) is a vowel I don't really recognize as English.