Most existing studies that employ social-trust information to solve the data sparsity issue in recommender systems assume that socially connected users have equal influence on each other. However, this assumption does not hold in practice since users and their friends may not have similar interests because social connections are multifaceted and exhibit heterogeneous strengths in different scenarios. Therefore, estimating the diverse levels of influence among entities (users/items/social connections) is very important in advancing social recommender systems. Towards this goal, we propose a new model named Social-Trust-Aware Variational Recommendation (SOAP-VAE). Particularly, SOAP-VAE leverages graph attention network techniques to capture the varying levels of influence and the complex interaction patterns among all the entities collectively and holistically. In doing so, heterogeneity among entities is obtained seamlessly. Consequently, we generate social-trustaware item embedding representations in which the right level of influence has been integrated. Next, based on these rich social-trust-aware item representations, we formulate the first-ever social-trust-aware prior in literature. Unlike priors utilized in earlier VAE-based recommendation models, this novel prior aids in dealing with the issue of posterior-collapse and can effectively capture the uncertainty of latent space. In effect, the model produces better latent representations, which significantly alleviates the data sparsity issue. Finally, we empirically show that SOAP-VAE outperforms several state-of-the-art baselines on three real-world data sets.