Yes, of course there are cases. The cases however, are not as numerous as other languages. For example -
I marks the direct object.
Ka kai au i te manu - I must eat the bird.
Hai marks the instrumental case e.g. -
He kai au hai to`oku rima - I ate with my hand
Subject case is generally 0, that is, unmarked -
Ka haere mai koe! - You must come!
Location case, is generally, by default, marked by i (past and present), ai (future), ō (from), mai (from), ki (to). These are the markers that I know that are location case markers.
I runga au - I was above.
Mai raro au - I have come from below
Ai reira tātou - We will be at that aforementioned place
Kihē? - To where?
Ōhē mai koe? - Where are you from?
These are some examples in Rapa Nui.
Dative and ablative don't apply in the majority of Polynesian languages, because 'i' always marks the direct object, even if you do switch with the subject (to make a VOS sentence), the meaning is still the same.
Linguicide IS genocide.
He ingoa ōpaki a Riki; he ingoa ōkawa a Ariki.
Riki is an informal name; Ariki is a formal name.