Because an adjective can be either strong or weak, it’s possible to write it several ways depending on what governs the sentence it appears in. However, because your characters will probably always be calling it “THE darkest night”, an article always governs the weak form. So, the four cases would yield myrkasta nóttin (nom), myrkustu nóttina (acc), myrkustu nóttinni (dat), myrkustu næturinnar (gen).
As for something more common I’m not too sure. Dimmur is another word for ‘dark’, and there’s a song in the animated movie ‘Anastasia’ called ‘Um niðdimma nótt’… niðdimmur and niðamyrkur both meaning something like ‘pitch dark’.
You might want to ask íslenskt mál just in case. It’s run by a native speaker with a degree in Icelandic.
The modern Icelandic alphabet has thirty-two letters, compared with twenty-six in modern English. There are two extra consonants (ð and þ), and an additional diphthong (æ). Readers may find a note on the pronounciations of specifically Icelandic letters helpful:
The pronunciation of the vowels is conditioned by the accents: