Machine learning finds rich applications in Internet of Things (IoT) networks such as information retrieval, traffic management, spectrum sensing, and signal authentication. While there is a surge of interest to understand the security issues of machine learning, their implications have not been understood yet for wireless applications such as those in IoT systems that are susceptible to various attacks due the open and broadcast nature of wireless communications. To support IoT systems with heterogeneous devices of different priorities, we present new techniques built upon adversarial machine learning and apply them to three types of over-the-air (OTA) wireless attacks, namely jamming, spectrum poisoning, and priority violation attacks. By observing the spectrum, the adversary starts with an exploratory attack to infer the channel access algorithm of an IoT transmitter by building a deep neural network classifier that predicts the transmission outcomes. Based on these prediction results, the wireless attack continues to either jam data transmissions or manipulate sensing results over the air (by transmitting during the sensing phase) to fool the transmitter into making wrong transmit decisions in the test phase (corresponding to an evasion attack). When the IoT transmitter collects sensing results as training data to retrain its channel access algorithm, the adversary launches a causative attack to manipulate the input data to the transmitter over the air. We show that these attacks with different levels of energy consumption and stealthiness lead to significant loss in throughput and success ratio in wireless communications for IoT systems. Then we introduce a defense mechanism that systematically increases the uncertainty of the adversary at the inference stage and improves the performance. Results provide new insights on how to attack and defend IoT networks using deep learning.