The record-breaking performance of deep neural networks (DNNs) comes with heavy parameterization, leading to external dynamic random-access memory (DRAM) for storage. The prohibitive energy of DRAM accesses makes it non-trivial to deploy DNN on resource-constrained devices, calling for minimizing the weight and data movements to improve the energy efficiency. We present SmartDeal (SD), an algorithm framework to trade higher-cost memory storage/access for lower-cost computation, in order to aggressively boost the storage and energy efficiency, for both inference and training. The core of SD is a novel weight decomposition with structural constraints, carefully crafted to unleash the hardware efficiency potential. Specifically, we decompose each weight tensor as the product of a small basis matrix and a large structurally sparse coefficient matrix whose non-zeros are quantized to power-of-2. The resulting sparse and quantized DNNs enjoy greatly reduced energy for data movement and weight storage, incurring minimal overhead to recover the original weights thanks to the sparse bit-operations and cost-favorable computations. Beyond inference, we take another leap to embrace energy-efficient training, introducing innovative techniques to address the unique roadblocks arising in training while preserving the SD structures. We also design a dedicated hardware accelerator to fully utilize the SD structure to improve the real energy efficiency and latency. We conduct experiments on both multiple tasks, models and datasets in different settings. Results show that: 1) applied to inference, SD achieves up to 2.44x energy efficiency as evaluated via real hardware implementations; 2) applied to training, SD leads to 10.56x and 4.48x reduction in the storage and training energy, with negligible accuracy loss compared to state-of-the-art training baselines. Our source codes are available online.