The brain tracks and encodes multi‐level speech features during spoken language processing. It is evident that this speech tracking is dominant at low frequencies (<8 Hz) including delta and theta bands. Recent research has demonstrated distinctions between delta‐ and theta‐band tracking but has not elucidated how they differentially encode speech across linguistic levels. Here, we hypothesised that delta‐band tracking encodes prediction errors (enhanced processing of unexpected features) while theta‐band tracking encodes neural sharpening (enhanced processing of expected features) when people perceive speech with different linguistic contents. EEG responses were recorded when normal‐hearing participants attended to continuous auditory stimuli that contained different phonological/morphological and semantic contents: (1) real‐words, (2) pseudo‐words and (3) time‐reversed speech. We employed multivariate temporal response functions to measure EEG reconstruction accuracies in response to acoustic (spectrogram), phonetic and phonemic features with the partialling procedure that singles out unique contributions of individual features. We found higher delta‐band accuracies for pseudo‐words than real‐words and time‐reversed speech, especially during encoding of phonetic features. Notably, individual time‐lag analyses showed that significantly higher accuracies for pseudo‐words than real‐words started at early processing stages for phonetic encoding (<100 ms post‐feature) and later stages for acoustic and phonemic encoding (>200 and 400 ms post‐feature, respectively). Theta‐band accuracies, on the other hand, were higher when stimuli had richer linguistic content (real‐words > pseudo‐words > time‐reversed speech). Such effects also started at early stages (<100 ms post‐feature) during encoding of all individual features or when all features were combined. We argue these results indicate that delta‐band tracking may play a role in predictive coding leading to greater tracking of pseudo‐words due to the presence of unexpected/unpredicted semantic information, while theta‐band tracking encodes sharpened signals caused by more expected phonological/morphological and semantic contents. Early presence of these effects reflects rapid computations of sharpening and prediction errors. Moreover, by measuring changes in EEG alpha power, we did not find evidence that the observed effects can be solitarily explained by attentional demands or listening efforts. Finally, we used directed information analyses to illustrate feedforward and feedback information transfers between prediction errors and sharpening across linguistic levels, showcasing how our results fit with the hierarchical Predictive Coding framework. Together, we suggest the distinct roles of delta and theta neural tracking for sharpening and predictive coding of multi‐level speech features during spoken language processing.