Recognizing the very size of the brain's circuits, hyperdimensional (HD) computing can model neural activity patterns with points in a HD space, that is, with HD vectors. Key examined properties of HD computing include: a versatile set of arithmetic operations on HD vectors, generality, scalability, analyzability, one-shot learning, and energy efficiency. These make it a prime candidate for efficient biosignal processing where signals are noisy and nonstationary, training data sets are not huge, individual variability is significant, and energy efficiency constraints are tight. Purely based on native HD computing operators, we describe a combined method for multiclass learning and classification of various ExG biosignals such as electromyography (EMG), electroencephalography (EEG), and electrocorticography (ECoG). We develop a full set of HD network templates that comprehensively encode body potentials and brain neural activity recorded from different electrodes into a single HD vector without requiring domain expert knowledge or ad-hoc electrode selection process. Such encoded HD vector is processed as a single unit for fast one-shot learning, and robust classification. It can be interpreted to identify the most useful features as well. Compared to state-of-the-art counterparts, HD computing enables online, incremental, and fast learning as it demands less than a third as much training data as well as less preprocessing.