There is an urgent need for automated methods to assist accurate and effective assessment of COVID-19. Radiology and nucleic acid test (NAT) are complementary COVID-19 diagnosis methods. In this paper, we present an end-to-end multitask learning (MTL) framework (COVID-MTL) that is capable of automated and simultaneous detection (against both radiology and NAT) and severity assessment of COVID-19. COVID-MTL learns different COVID-19 tasks in parallel through our novel random-weighted loss function, which assigns learning weights under Dirichlet distribution to prevent task dominance; our new 3D real-time augmentation algorithm (Shift3D) introduces space variances for 3D CNN components by shifting low-level feature representations of volumetric inputs in three dimensions; thereby, the MTL framework is able to accelerate convergence and improve joint learning performance compared to single-task models. By only using chest CT scans, COVID-MTL was trained on 930 CT scans and tested on separate 399 cases. COVID-MTL achieved AUCs of 0.939 and 0.846, and accuracies of 90.23% and 79.20% for detection of COVID-19 against radiology and NAT, respectively, which outperformed the state-of-the-art models. Meanwhile, COVID-MTL yielded AUC of 0.800 $\pm$ 0.020 and 0.813 $\pm$ 0.021 (with transfer learning) for classifying control/suspected, mild/regular, and severe/critically-ill cases. To decipher the recognition mechanism, we also identified high-throughput lung features that were significantly related (P < 0.001) to the positivity and severity of COVID-19.