The rising demand for energy-efficient edge AI systems (e.g., mobile agents/robots) has increased the interest in neuromorphic computing, since it offers ultra-low power/energy AI computation through spiking neural network (SNN) algorithms on neuromorphic processors. However, their efficient implementation strategy has not been comprehensively studied, hence limiting SNN deployments for edge AI systems. Toward this, we propose a design methodology to enable efficient SNN processing on commodity neuromorphic processors. To do this, we first study the key characteristics of targeted neuromorphic hardware (e.g., memory and compute budgets), and leverage this information to perform compatibility analysis for network selection. Afterward, we employ a mapping strategy for efficient SNN implementation on the targeted processor. Furthermore, we incorporate an efficient on-chip learning mechanism to update the systems' knowledge for adapting to new input classes and dynamic environments. The experimental results show that the proposed methodology leads the system to achieve low latency of inference (i.e., less than 50ms for image classification, less than 200ms for real-time object detection in video streaming, and less than 1ms in keyword recognition) and low latency of on-chip learning (i.e., less than 2ms for keyword recognition), while incurring less than 250mW of processing power and less than 15mJ of energy consumption across the respective different applications and scenarios. These results show the potential of the proposed methodology in enabling efficient edge AI systems for diverse application use-cases.