Does Annie and finnick odair get married?

Yes.

This happens in the third book in The Hunger Games series, Mockingjay. Finnick and Annie get married in District 13, and Peeta Mellark bakes their wedding cake. Finnick wears one of Peeta's suits. Annie wears Katniss's outfit from visiting District 5. Later on, Finnick dies, and Annie has a baby. The baby is Finnick's.