As a certified Dane I should be able to help, but like Artell I can't come up with any English words with the same sound. In fact, there's a myth saying that during World War 2 the Danes would find German spies by making them say the phrase 'rødgrød med fløde' which only native Danes could ever get right. The story is not true, but it serves to illustrate just how alien the pronunciation is to non-Scandinavians.

But I digress. On this page you can hear the pronunciation of all the letters in Danish. http://www.speakdanish.dk/en/pronunciation/alphabet.php

Being on student exchange in Denmark helps though.

A lot of the time it varies on the word, but for Søren, it's typically an 'Eu' sound, though that varies on who's saying it.

It's pronounced like the Finnish or Swedish Ö.

Oh wait, I guess that's not very useful? I can't think of any English approximation for it; I can't even think of an English word that would have that sound. Try looking for a recording of the pronunciation online?

As is Wikipedia.

A quick little search shows a bunch of results of people asking that question and getting answers.