Sophisticated learning architectures, e.g., Transformers, present a unique opportunity for robots to understand complex vehicle-terrain kinodynamic interactions for off-road mobility. While internet-scale data are available for Natural Language Processing (NLP) and Computer Vision (CV) tasks to train Transformers, real-world mobility data are difficult to acquire with physical robots navigating off-road terrain. Furthermore, training techniques specifically designed to process text and image data in NLP and CV may not apply to robot mobility. In this paper, we propose VertiFormer, a novel data-efficient multi-task Transformer model trained with only one hour of data to address such challenges of applying Transformer architectures for robot mobility on extremely rugged, vertically challenging, off-road terrain. Specifically, VertiFormer employs a new learnable masked modeling and next token prediction paradigm to predict the next pose, action, and terrain patch to enable a variety of off-road mobility tasks simultaneously, e.g., forward and inverse kinodynamics modeling. The non-autoregressive design mitigates computational bottlenecks and error propagation associated with autoregressive models. VertiFormer's unified modality representation also enhances learning of diverse temporal mappings and state representations, which, combined with multiple objective functions, further improves model generalization. Our experiments offer insights into effectively utilizing Transformers for off-road robot mobility with limited data and demonstrate our efficiently trained Transformer can facilitate multiple off-road mobility tasks onboard a physical mobile robot.