Given an input video, its associated audio, and a brief caption, the audio-visual scene aware dialog (AVSD) task requires an agent to indulge in a question-answer dialog with a human about the audio-visual content. This task thus poses a challenging multi-modal representation learning and reasoning scenario, advancements into which could influence several human-machine interaction applications. To solve this task, we introduce a semantics-controlled multi-modal shuffled Transformer reasoning framework, consisting of a sequence of Transformer modules, each taking a modality as input and producing representations conditioned on the input question. Our proposed Transformer variant uses a shuffling scheme on their multi-head outputs, demonstrating better regularization. To encode fine-grained visual information, we present a novel dynamic scene graph representation learning pipeline that consists of an intra-frame reasoning layer producing spatio-semantic graph representations for every frame, and an inter-frame aggregation module capturing temporal cues. Our entire pipeline is trained end-to-end. We present experiments on the benchmark AVSD dataset, both on answer generation and selection tasks. Our results demonstrate state-of-the-art performances on all evaluation metrics.