Sound events have semantic identities, locations, and trajectories, yet existing audio-language models typically encode clips as global event content. Conversely, sound event localization models track source directions over time but offer limited semantic coverage for language reasoning. To bridge this gap, we introduce ST-AudioQA, a spatio-temporal audio QA dataset and benchmark built from first-order ambisonic (FOA) renderings of static and moving sound sources. Each scene provides source identity, activity, direction, distance, and motion metadata, enabling dense trajectory supervision and QA about what is sounding, where it is, how it moves, and how sources relate. We further introduce ST-Audio Encoder, which jointly learns event semantics and time-resolved source trajectories, and ST-AudioLM, which exposes these audio tokens to an LLM for spatio-temporal audio QA. Experiments show that this representation improves the balance between semantic preservation and localization and yields stronger reasoning than static spatial and localization-oriented baselines. Beyond the controlled benchmark, ST-AudioLM shows zero-shot transfer to real recordings, with further gains after light adaptation. Project page: https://st-audiolm.github.io/.