This study proposes different deep learning approaches to automatically classify pneumoconiosis based on the International Labour Office ("ILO") classification system. Through collaboration with the National Institute for Occupational Safety and Health (NIOSH), this study curated a custom dataset of chest radiographs with (N=520) and without (N=149) pneumoconiosis. The four-point major category scale of profusion (concentration) of small opacities (0, 1, 2, or 3) were considered in this study. Several deep learning models were evaluated for classifying different levels of profusion grades including: 1) Transfer learning with models pre-trained with public chest radiograph repositories, 2) Hand-crafted radiomic feature extraction, and 3) Hybrid architecture that integrates hand-crafted radiomic features with transfer-learned features using a loss function that incorporates the inherent ordinality within the profusion grade scale. For profusion grade 0 vs. grade 3, both the transfer learning and radiomic feature extraction methods obtained test-set accuracies of greater than 91%. The highest prediction accuracy for normal (profusion grade 0) vs. abnormal (profusion grade 1, 2 and 3) was 83% using the transfer learning method. Under the setting of multi-class identification of four profusion grades, ResNet model adapted to a ordinal multi-task loss function notably outperforms traditional models reliant on cross-entropy loss (with accuracy 58%) and achieves an accuracy of approximately 61%. The amalgamation of radiomic and ResNetderived features, coupled with the application of multi-task loss, culminates in the highest recorded accuracy of approximately 62%. This demonstrates an example case where the integration of hand-crafted and deeplearned features, along with modeling the ordinality of the classes, improves classification performance of chest radiographs.