Well, seeing
Eirik in print on this board, I wondered if it was a variant of
Erik. If I saw it in a local U.S. newspaper's birth announcement, I would probably still wonder that, but also would think the parents might have chosen this spelling to cause a different pronunciation.
Just based on phonetics alone, I would probably read
Eirik with the first syllable sounding like "eye". Some words with "ei" are pronounced with a long "a" sound, like "reign", but the long "i", like "height" is what strikes me first.