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Off-policy policy optimization is a challenging problem in reinforcement learning (RL). The algorithms designed for this problem often suffer from high variance in their estimators, which results in poor sample efficiency, and have issues with convergence. A few variance-reduced on-policy policy gradient algorithms have been recently proposed that use methods from stochastic optimization to reduce the variance of the gradient estimate in the REINFORCE algorithm. However, these algorithms are not designed for the off-policy setting and are memory-inefficient, since they need to collect and store a large ``reference'' batch of samples from time to time. To achieve variance-reduced off-policy-stable policy optimization, we propose an algorithm family that is memory-efficient, stochastically variance-reduced, and capable of learning from off-policy samples. Empirical studies validate the effectiveness of the proposed approaches.