The growing volume of end-of-life rubber and polymer waste from the automotive sector, combined with increasing demand for acoustic comfort in buildings, motivates the development of sustainable composite materials that integrate waste valorization with improved functional performance. The objective of this study was to systematically compare the effect of nine distinct types of recycled rubber and polymer waste granules — including tire rubber, rubber seals, painted and unpainted bumpers, fuel tanks, and cable insulation — introduced at 10% by volume into the core layer of three-layer particleboard, on the sound absorption properties of the resulting composites. Samples with a thickness of 18 mm were tested using the impedance tube method in accordance with ISO 10534-2 over the frequency range of 125–4000 Hz. Acoustic performance was evaluated using the frequency-dependent sound absorption coefficient α(f), the weighted absorption coefficient αw (ISO 11654), and the NRC index (ASTM C423). The results showed an increase in absorption with frequency, consistent with porous composite behavior. Among all variants, granules from waste rubber seals (SCG) achieved the highest performance, reaching an average value of α = 0.251 in the range of 1000–2000 Hz and NRC = 0.35, which represents an improvement of approximately 80% compared to the unmodified reference board (NRC = 0.15). Tire-derived granules (T, TG) demonstrated stable broadband effectiveness (NRC = 0.30), while the addition of graphite did not yield statistically significant improvement. Rigid polymer granules (painted bumpers, cable insulation) showed no meaningful acoustic enhancement. One-way ANOVA with Tukey HSD post-hoc analysis confirmed statistically significant differences (p < 0.001, partial η² = 0.78) between rubber-based and polymer-based modifier groups in the 1000–2000 Hz range. The maximum αw value of 0.20 classifies the best-performing variants as class E (ISO 11654). Although absolute absorption remains moderate, the results demonstrate that selected elastomeric waste fractions can meaningfully enhance the sound-damping properties of structural particleboard, positioning these composites as functional elements in layered building systems within a circular economy framework.