Bjork is Icelandic, Bjerke norwegian, and they both mean [name]Birch[/name] which is a gorgeous name in it’s own right. Bjerke is my mom’s family names, and I’ve always been slightly dissapointed that while she didn’t pass it on to any of her children in any way, so much so that I have considered adding it on to my own as a 2nd middle name. I’ve always felt a strong attachment to my maternal grandfather and my Norwegian ancestry, and even though it has obvious pronounciation issues (people always called my house looking for a Mrs. ‘Buhjerkee’ (it’s more like Byurk) I’m definitely going to incorporate it into my first child’s name somehow but I’m not sure how I’d do it.
A middle name like [name]Sebastien[/name] Bjerke or [name]Hollis[/name] Bjerke is gorgeous [name]IMO[/name] but [name]Birch[/name] is also great as a first name, though obviously there’s the potential for cruel kids to turn it into Bitch. And Bjork is much more widely recognized and properly pronounced.
What’s your OPs?
[name]Hi[/name] there! [name]How[/name] lovely to honor your heritage! If you’re going to use Bjereke or Bjork, I’d use those spellings as a middle name, just as you suggested. [name]Sebastien[/name] Bjerek and [name]Hollis[/name] Bjerke are lovely, and it sounds as thought you’re already aware of having to correct people’s pronunciation.
[name]Birch[/name] is a great idea for a first name, but only on a boy, as I’d worry about people calling a female [name]Birch[/name] a closely related not-so-nice name.
I’m not familiar with other Norwegian or Icelandic names other than [name]Birgitte[/name] and possibly [name]Beatrix[/name] or [name]Katya[/name], but the names you’ve listed above are great!
Best wishes to you! 
I agree with [name]Jill[/name] one both points. [name]Birch[/name] is very cute for a boy or would make a great middle on either a boy or girl.