Learn Icelandic: Ég á eftir að hita okkur kaffið. - I still have to heat the coffee for us.

This is the dative of advantage (dativus commodi). Instead of using a preposition to say you are doing something "for" someone, Icelandic often just puts the person benefiting from the action straight into the dative case.

Does the dative of advantage always go before the direct object, like okkur comes before kaffið?

Yes, structurally it acts just like an indirect object. The dative pronoun or noun showing who benefits comes right after the verb and before the accusative direct object.

The translation says "I still have to", but how does ég á eftir að literally work?

The phrase eiga eftir að literally translates to "to own after to". It is a very common Icelandic idiom used to say that an action remains to be done, meaning you "have yet to" do it or "still have to" do it.

Why is kaffið in the definite form here?

While English speakers often just say "heat us coffee" in this context, Icelandic strongly prefers the definite article when referring to a specific, expected batch of food or drink that is about to be prepared or served.