We present a novel framework that can combine multi-domain learning (MDL), data imputation (DI) and multi-task learning (MTL) to improve performance for classification and regression tasks in different domains. The core of our method is an adversarial autoencoder that can: (1) learn to produce domain-invariant embeddings to reduce the difference between domains; (2) learn the data distribution for each domain and correctly perform data imputation on missing data. For MDL, we use the Maximum Mean Discrepancy (MMD) measure to align the domain distributions. For DI, we use an adversarial approach where a generator fill in information for missing data and a discriminator tries to distinguish between real and imputed values. Finally, using the universal feature representation in the embeddings, we train a classifier using MTL that given input from any domain, can predict labels for all domains. We demonstrate the superior performance of our approach compared to other state-of-art methods in three distinct settings, DG-DI in image recognition with unstructured data, MTL-DI in grade estimation with structured data and MDMTL-DI in a selection process using mixed data.