Learn Icelandic: Galleríið kaupir málverkið af merkilegum listamönnum. - The gallery buys the painting from remarkable artists.

It modifies listamönnum, which is in the dative plural. When an adjective describes an indefinite plural noun in the dative case, it takes the strong ending -um. The great news for learners is that this dative plural -um ending is exactly the same for all three genders!

Why are the artists in the dative case here?

They are in the dative case because of the preposition af (from). In Icelandic, af always forces the following noun phrase into the dative case, which is why both the adjective merkilegum and the noun listamönnum take dative endings.

I know the singular for artist is listamaður. Why does the dative plural have an ö in listamönnum?

This is caused by the -um ending itself. The u in the ending triggers a sound change called U-mutation, which pulls the root vowel a in the base word toward the back of the mouth, turning it into an ö. This happens in almost all dative plural nouns that have an a in their root!

Is málverkið (the painting) in the nominative or accusative case?

It is in the accusative case because it is the direct object of the verb kaupir (buys). However, because málverk is a neuter noun, its nominative and accusative forms are identical, even with the definite article -ið attached.