Learn Icelandic: Þeir eru ekki þreyttir. - They masculine are not tired.

Icelandic has three different words for "they" depending on gender. Þeir is strictly masculine, meaning the group being talked about consists only of males (or grammatically masculine nouns). If it were a group of females, you would use þær, and for a mixed-gender group or neuter nouns, you use þau.

Is the verb eru only used with þeir?

No, eru is the form of the verb að vera (to be) for almost all plural pronouns! It is used for all versions of "they" (þeir, þær, þau) and also for "you all" (þið). The only plural pronoun that uses a different form is "we" (við erum).

Why does the word for tired end in -ir (þreyttir)?

Adjectives in Icelandic must match the gender and number (singular or plural) of the subject they describe. Since þeir is a masculine plural pronoun, the base adjective þreyttur (tired) drops its singular ending and adds the masculine plural ending -ir to become þreyttir.

Where does ekki go in a negative sentence like this?

In simple statements, ekki (not) comes directly after the verb. Just like in English where you say "are not", in Icelandic you put ekki immediately after the verb eru.