Hello! My friend who is a vegetarian dined here with me on my birthday so I can share some information with you. It is not needed to call ahead and they do have some different options. She was not vegan and does occasionally eat chicken, so I do not know how it would fit into a vegan stand point. She was offered a different appetizer of assorted hummus and vegetables/pitas and I believe she could have the salad and the bread. She was given an entree that was a huge vegetable and pasta dish with tofu dish that she said was absolutely delicious. I know I have seen photos on the internet before so you may want to try searching. She was very pleased and I think as long as you don't mind others eating the meat, as they come around with it on big skewers to your table you can still enjoy the restaurant.
This link has some information, some is related to vegan, but also gluten and dairy free as well so mileage may vary, but should give you a general idea
http://www.glutenfreedairyfreewdw.com/ohana-dinner-table-service-polynesian/