I learned this weekend that “nei” can only be used as a response rather than used in a sentence.
This learning moment came about when I mistakenly said “nei Íslendingar” in a sentence and my friend corrected me, noting what I should have said is “engir Íslendingar.” Later, I grew curious as to why “engir” (masculine) would be used instead of “engin” (neuter), as saying “engir Íslendingar” implies a general group of people. My tutor later informed me that when you’re speaking about an unspecified person or group, the default is always masculine.
You can say “nei” in a sentence if you’re objecting to something, my friend told me, such as: “Nei, það er ekki rétt.” But that’s about it, it seems.
“Einhver” means someone/somebody, and “enginn” means no one/nobody/none (as a pronoun). The screenshot below explains it in more detail.

And with that, I promise to never use “nei” in an Icelandic sentence again! 😛