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Human activity recognition (HAR) from wearable sensors data has become ubiquitous due to the widespread proliferation of IoT and wearable devices. However, recognizing human activity in heterogeneous environments, for example, with sensors of different models and make, across different persons and their on-body sensor placements introduces wide range discrepancies in the data distributions, and therefore, leads to an increased error margin. Transductive transfer learning techniques such as domain adaptation have been quite successful in mitigating the domain discrepancies between the source and target domain distributions without the costly target domain data annotations. However, little exploration has been done when multiple distinct source domains are present, and the optimum mapping to the target domain from each source is not apparent. In this paper, we propose a deep Multi-Source Adversarial Domain Adaptation (MSADA) framework that opportunistically helps select the most relevant feature representations from multiple source domains and establish such mappings to the target domain by learning the perplexity scores. We showcase that the learned mappings can actually reflect our prior knowledge on the semantic relationships between the domains, indicating that MSADA can be employed as a powerful tool for exploratory activity data analysis. We empirically demonstrate that our proposed multi-source domain adaptation approach achieves 2% improvement with OPPORTUNITY dataset (cross-person heterogeneity, 4 ADLs), whereas 13% improvement on DSADS dataset (cross-position heterogeneity, 10 ADLs and sports activities).