Despite achieving remarkable success in various domains, recent studies have uncovered the vulnerability of deep neural networks to adversarial perturbations, creating concerns on model generalizability and new threats such as prediction-evasive misclassification or stealthy reprogramming. Among different defense proposals, stochastic network defenses such as random neuron activation pruning or random perturbation to layer inputs are shown to be promising for attack mitigation. However, one critical drawback of current defenses is that the robustness enhancement is at the cost of noticeable performance degradation on legitimate data, e.g., large drop in test accuracy. This paper is motivated by pursuing for a better tradeoff between adversarial robustness and test accuracy for stochastic network defenses. We propose Defense Efficiency Score (DES), a comprehensive metric that measures the gain in unsuccessful attack attempts at the cost of drop in test accuracy of any defense. To achieve a better DES, we propose hierarchical random switching (HRS), which protects neural networks through a novel randomization scheme. A HRS-protected model contains several blocks of randomly switching channels to prevent adversaries from exploiting fixed model structures and parameters for their malicious purposes. Extensive experiments show that HRS is superior in defending against state-of-the-art white-box and adaptive adversarial misclassification attacks. We also demonstrate the effectiveness of HRS in defending adversarial reprogramming, which is the first defense against adversarial programs. Moreover, in most settings the average DES of HRS is at least 5 higher than current stochastic network defenses, validating its significantly improved robustness-accuracy trade-off.