Recent advance in wearable electronics has contributed to the rapidly increasing interest for the Internet of Things (IoTs) that can consistently monitor signals. For realization of IoTs, the devices should possess sufficient stretchability to attach conformably to any nonplanar objects. In addition, optical transparency is also required to improve the natural look of the devices. In this regard, the conventional transparent conductor must be substituted by stretchable transparent electrodes for wearable devices. For this purpose, we chose metal nanowires (mNW)-graphene hybrid nanostructures due to their superb electrical conductivity (<30 Ω/sq), transparency (>90%), and stretchability. As another key function of IoTs, the wearable devices are required to accompany wireless communication systems for consistent monitoring. For this function, sensors should always transmit acquired data to users for interaction. Here, we report the realization of stretchable graphene sensors based on the silver nanowire-graphene hybrid nanostructures. The device shows high stretchability and transparency while maintaining their sensing capability for the simulant of nerve agent (dimethyl methylphosphonate). The fabricated sensors show outstanding sensing parameters (e.g., sensitivity and recovery, etc.). Furthermore, in order to realize IoTs which can monitor environments continuously, we integrated the sensors with wireless communication systems (Bluetooth and inductive antennas). The integrated sensors also retain high sensing performances on the nonplanar objects (e.g., leaves of live plant). We believe that the realization of wearable and wireless gas sensors suggests a promising strategy toward IoT devices.