The use of synthetic data in indoor 3D object detection offers the potential of greatly reducing the manual labor involved in 3D annotations and training effective zero-shot detectors. However, the complicated domain shifts across syn-to-real indoor datasets remains underexplored. In this paper, we propose a novel Object-wise Hierarchical Domain Alignment (OHDA) framework for syn-to-real unsupervised domain adaptation in indoor 3D object detection. Our approach includes an object-aware augmentation strategy to effectively diversify the source domain data, and we introduce a two-branch adaptation framework consisting of an adversarial training branch and a pseudo labeling branch, in order to simultaneously reach holistic-level and class-level domain alignment. The pseudo labeling is further refined through two proposed schemes specifically designed for indoor UDA. Our adaptation results from synthetic dataset 3D-FRONT to real-world datasets ScanNetV2 and SUN RGB-D demonstrate remarkable mAP25 improvements of 9.7% and 9.1% over Source-Only baselines, respectively, and consistently outperform the methods adapted from 2D and 3D outdoor scenarios. The code will be publicly available upon paper acceptance.