The conventional wisdom has been that designing ultra-compact, battery-constrained wireless hearables with on-device speech AI models is challenging due to the high computational demands of streaming deep learning models. Speech AI models require continuous, real-time audio processing, imposing strict computational and I/O constraints. We present NeuralAids, a fully on-device speech AI system for wireless hearables, enabling real-time speech enhancement and denoising on compact, battery-constrained devices. Our system bridges the gap between state-of-the-art deep learning for speech enhancement and low-power AI hardware by making three key technical contributions: 1) a wireless hearable platform integrating a speech AI accelerator for efficient on-device streaming inference, 2) an optimized dual-path neural network designed for low-latency, high-quality speech enhancement, and 3) a hardware-software co-design that uses mixed-precision quantization and quantization-aware training to achieve real-time performance under strict power constraints. Our system processes 6 ms audio chunks in real-time, achieving an inference time of 5.54 ms while consuming 71.6 mW. In real-world evaluations, including a user study with 28 participants, our system outperforms prior on-device models in speech quality and noise suppression, paving the way for next-generation intelligent wireless hearables that can enhance hearing entirely on-device.