We investigated how neural oscillations code the hierarchical nature of stress rhythms in speech and how stress processing varies with language experience. By measuring phase synchrony of multilevel EEG-acoustic tracking and intra-brain cross-frequency coupling, we show the encoding of stress involves different neural signatures (delta rhythms = stress foot rate; theta rhythms = syllable rate), is stronger for amplitude vs. duration stress cues, and induces nested delta-theta coherence mirroring the stress-syllable hierarchy in speech. Only native English, but not Mandarin, speakers exhibited enhanced neural entrainment at central stress (2 Hz) and syllable (4 Hz) rates intrinsic to natural English. English individuals with superior cortical-stress tracking capabilities also displayed stronger neural hierarchical coherence, highlighting a nuanced interplay between internal nesting of brain rhythms and external entrainment rooted in language-specific speech rhythms. Our cross-language findings reveal brain-speech synchronization is not purely a "bottom-up" but benefits from "top-down" processing from listeners' language-specific experience.