This paper focuses on the analysis of an optimal sensing and quantization strategy in a multi-sensor network where each individual sensor sends its quantized log-likelihood information to the fusion center (FC) for non-Bayesian quickest change detection. It is assumed that the sensors are equipped with a battery/energy storage device of finite capacity, capable of harvesting energy from the environment. The FC is assumed to have access to either non-causal or causal channel state information (CSI) and energy state information (ESI) from all the sensors while performing the quickest change detection. The primary observations are assumed to be generated from a sequence of random variables whose probability distribution function changes at an unknown time point. The objective of the detection problem is to minimize the average detection delay of the change point with respect to a lower bound on the rate of false alarm. In this framework, the optimal sensing decision and number of quantization bits for information transmission can be determined with the constraint of limited available energy due to finite battery capacity. This optimization is formulated as a stochastic control problem and is solved using dynamic programming algorithms for both non-causal and causal CSI and ESI scenario. A set of non-linear equations is also derived to determine the optimal quantization thresholds for the sensor log-likelihood ratios, by maximizing an appropriate Kullback-Leibler (KL) divergence measure between the distributions before and after the change. A uniform threshold quantization strategy is also proposed as a simple sub-optimal policy. The simulation results indicate that the optimal quantization is preferable when the number of quantization bits is low as its performance is significantly better compared to its uniform counterpart in terms of average detection delay. For the case of a large number of quantization bits, the performance benefits of using the optimal quantization as compared to its uniform counterpart diminish, as expected.