How language mediates emotional perception and experience is poorly understood. The present event-related potential (ERP) study examined the explicit and implicit processing of emotional speech to differentiate the relative influences of communication channel, emotion category and task type in the prosodic salience effect. Thirty participants (15 women) were presented with spoken words denoting happiness, sadness and neutrality in either the prosodic or semantic channel. They were asked to judge the emotional content (explicit task) and speakers’ gender (implicit task) of the stimuli. Results indicated that emotional prosody (relative to semantics) triggered larger N100 and P200 amplitudes with greater delta, theta and alpha inter-trial phase coherence (ITPC) values in the corresponding early time windows, and continued to produce larger LPC amplitudes and faster responses during late stages of higher-order cognitive processing. The relative salience of prosodic and semantics was modulated by emotion and task, though such modulatory effects varied across different processing stages. The prosodic salience effect was reduced for sadness processing and in the implicit task during early auditory processing and decision-making but reduced for happiness processing in the explicit task during conscious emotion processing. Additionally, across-trial synchronization of delta, theta and alpha bands predicted the ERP components with higher ITPC values significantly associated with stronger N100, P200 and LPC enhancement. These findings reveal the neurocognitive dynamics of emotional speech processing with prosodic salience tied to stage-dependent emotion- and task-specific effects, which can reveal insights to research reconciling language and emotion processing from cross-linguistic/cultural and clinical perspectives.