We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.