Not really a genealogical reply, but just a note.
The ð in Eiði is NOT pronunced like the Icelandic ð (English th in the). In Faroese this sound has been lost, and today ð mostly represents a hiatus. In this case a y-sound.
Thus Eiði is pronunced EYE-YUH. (or if you live in Eiði it's pronunced OY-YUH) :)
Also, Faroese is a case languages, yes, but its endings don't change to a such extent as they do in e.g. Russian or Finnish.
Just wanted to point these things out. :)