Integrated Sensing and Communication (ISAC) is a technology paradigm that combines sensing capabilities with communication functionalities in a single device or system. In vehicle-to-everything (V2X) sidelink, ISAC can provide enhanced safety by allowing vehicles to not only communicate with one another but also sense the surrounding environment by using sidelink signals. In ISAC-capable V2X sidelink, the random resource allocation results in an unstructured and sparse distribution of time and frequency resources in the received orthogonal frequency division multiplexing (OFDM) grid, leading to degraded radar detection performance when processed using the conventional 2D-FFT method. To address this challenge, this paper proposes a high-resolution off-grid radar target detection algorithm irrespective of the OFDM grid structure. The proposed method utilizes the Newtonized orthogonal matching pursuit (NOMP) algorithm to effectively detect weak targets masked by the sidelobes of stronger ones and accurately estimates off-grid range and velocity parameters with minimal resources through Newton refinements. Simulation results demonstrate the superior performance of the proposed NOMP-based target detection algorithm compared to existing compressed sensing (CS) methods in terms of detection probability, resolution, and accuracy. Additionally, experimental validation is performed using a bi-static radar setup in a semi-anechoic chamber. The measurement results validate the simulation findings, showing that the proposed algorithm significantly enhances target detection and parameter estimation accuracy in realistic scenarios.