The prevailing of artificial intelligence-of-things calls for higher energy-efficient edge computing paradigms, such as neuromorphic agents leveraging brain-inspired spiking neural network (SNN) models based on spatiotemporally sparse binary activations. However, the lack of efficient and high-accuracy deep SNN learning algorithms prevents them from practical edge deployments with a strictly bounded cost. In this paper, we propose a spatiotemporal orthogonal propagation (STOP) algorithm to tack this challenge. Our algorithm enables fully synergistic learning of synaptic weights as well as firing thresholds and leakage factors in spiking neurons to improve SNN accuracy, while under a unified temporally-forward trace-based framework to mitigate the huge memory requirement for storing neural states of all time-steps in the forward pass. Characteristically, the spatially-backward neuronal errors and temporally-forward traces propagate orthogonally to and independently of each other, substantially reducing computational overhead. Our STOP algorithm obtained high recognition accuracies of 99.53%, 94.84%, 74.92%, 98.26% and 77.10% on the MNIST, CIFAR-10, CIFAR-100, DVS-Gesture and DVS-CIFAR10 datasets with adequate SNNs of intermediate scales from LeNet-5 to ResNet-18. Compared with other deep SNN training works, our method is more plausible for edge intelligent scenarios where resources are limited but high-accuracy in-situ learning is desired.