Diverse types of edge data, such as 2D geo-locations and 3D point clouds, are collected by sensors like lidar and GPS receivers on edge devices. On-device searches, such as k-nearest neighbor (kNN) search and radius search, are commonly used to enable fast analytics and learning technologies, such as k-means dataset simplification using kNN. To maintain high search efficiency, a representative approach is to utilize a balanced multi-way KD-tree (BMKD-tree). However, the index has shown limited gains, mainly due to substantial construction overhead, inflexibility to real-time insertion, and inconsistent query performance. In this paper, we propose UnIS to address the above limitations. We first accelerate the construction process of the BMKD-tree by utilizing the dataset distribution to predict the splitting hyperplanes. To make the continuously generated data searchable, we propose a selective sub-tree rebuilding scheme to accelerate rebalancing during insertion by reducing the number of data points involved. We then propose an auto-selection model to improve query performance by automatically selecting the optimal search strategy among multiple strategies for an arbitrary query task. Experimental results show that UnIS achieves average speedups of 17.96x in index construction, 1.60x in insertion, 7.15x in kNN search, and 1.09x in radius search compared to the BMKD-tree. We further verify its effectiveness in accelerating dataset simplification on edge devices, achieving a speedup of 217x over Lloyd's algorithm.