A major challenge involved in automatic dysarthria severity classification for patients with Amyotrophic Lateral Sclerosis (ALS) is the difficulty to build a speech corpus which is large enough to train accurate and generalizable classifiers. To overcome this constraint, we employ transfer learning approaches, specifically, fine-tuning from an auxiliary task and multi-task learning. Input feature reconstruction and gender classification, on the same ALS speech dataset or other healthy speech corpora, are explored as the auxiliary tasks. We use temporal statistics of mel-frequency cepstral coefficients as the features and dense neural networks for performing the primary and auxiliary tasks. Experiments suggest that transfer learning aids severity classification with up to 11.03% absolute increase in the average classification accuracy as compared to direct single task learning. The improvement is attributed mainly to better classification of the mild class than severe/normal classes.