This paper presents a novel multi-modal learning approach for automated skill characterization of obstetric ultrasound operators using heterogeneous spatio-temporal sensory cues, namely, scan video, eye-tracking data, and pupillometric data, acquired in the clinical environment. We address pertinent challenges such as combining heterogeneous, small-scale and variable-length sequential datasets, to learn deep convolutional neural networks in real-world scenarios. We propose spatial encoding for multi-modal analysis using sonography standard plane images, spatial gaze maps, gaze trajectory images, and pupillary response images. We present and compare five multi-modal learning network architectures using late, intermediate, hybrid, and tensor fusion. We build models for the Heart and the Brain scanning tasks, and performance evaluation suggests that multi-modal learning networks outperform uni-modal networks, with the best-performing model achieving accuracies of 82.4% (Brain task) and 76.4% (Heart task) for the operator skill classification problem.