We study the problem of processing continuous k nearest neighbor (CkNN) queries over moving objects on road networks, which is an essential operation in a variety of applications. We are particularly concerned with scenarios where the object densities in different parts of the road network evolve over time as the objects move. Existing methods on CkNN query processing are ill-suited for such scenarios as they utilize index structures with fixed granularities and are thus unable to keep up with the evolving object densities. In this paper, we directly address this problem and propose an object density aware index structure called ODIN that is an elastic tree built on a hierarchical partitioning of the road network. It is equipped with the unique capability of dynamically folding/unfolding its nodes, thereby adapting to varying object densities. We further present the ODIN-KNN-Init and ODIN-KNN-Inc algorithms for the initial identification of the kNNs and the incremental update of query result as objects move. Thorough experiments on both real and synthetic datasets confirm the superiority of our proposal over several baseline methods.