my informed guess and yet I'm sure some Scandinavian will correct me:
Neels (with short EE, like in Nina)
Hè-ning (Hè with short è, like in Men; "ning" like the Ming vase)
Orsted, has a / through the O, which (AFAIK) means that it is pronounced like the German Ö, just like the Swedish cook does all the time, you know the "eh..." like you're thinking what to say next. Much like the French "eu" in Bleu, but shorter. I would expect there is a tiny more emphasis on the second syllable than none at all. Just to make it all more difficult of course, I'm sure.
Pèdersen, has the emphasis on the first syllable and on nothing else. The "e" in "Ped" is short, much like the one in Henning. "ederson" just flows away, like in the English name Petersen, or Ronaldson, or Whateverson.