Inspite the emerging importance of Speech Emotion Recognition (SER), the state-of-the-art accuracy is quite low and needs improvement to make commercial applications of SER viable. A key underlying reason for the low accuracy is the scarcity of emotion datasets, which is a challenge for developing any robust machine learning model in general. In this paper, we propose a solution to this problem: a multi-task learning framework that uses auxiliary tasks for which data is abundantly available. We show that utilisation of this additional data can improve the primary task of SER for which only limited labelled data is available. In particular, we use gender identifications and speaker recognition as auxiliary tasks, which allow the use of very large datasets, e.g., speaker classification datasets. To maximise the benefit of multi-task learning, we further use an adversarial autoencoder (AAE) within our framework, which has a strong capability to learn powerful and discriminative features. Furthermore, the unsupervised AAE in combination with the supervised classification networks enables semi-supervised learning which incorporates a discriminative component in the AAE unsupervised training pipeline. This semi-supervised learning essentially helps to improve generalisation of our framework and thus leads to improvements in SER performance. The proposed model is rigorously evaluated for categorical and dimensional emotion, and cross-corpus scenarios. Experimental results demonstrate that the proposed model achieves state-of-the-art performance on two publicly available datasets.