The experimental development of thin films that exhibit higher room-temperature low-field magnetoelectric (ME) sensing without compromising reliable electrical energy storage capabilities is rare. Here, an improved ferroelectric polarization, ME coupling and energy storage performance of polymer-based nanocomposites, which find applications in portable high-power dielectric capacitors, are studied. Multiferroic nanofiller-based three-phase flexible nanocomposites, polyvinylidene fluoride (PVDF)-(Ba0.7Ca0.3)TiO3-(Co0.6Zn0.4)Fe2O4, were fabricated using compression molding to enhance polarization which is pivotal for applications. PVDF with a high β-phase content (92.4 %), switchable ferroelectric behavior and higher breakdown strength (510 kV/mm) was obtained under optimized process conditions (500 MPa at 165 °C). The fabrication assisted alteration of intermolecular chain distance results in a tensile strain (1.42 %) of β-crystallites corresponding to an internal stress of ~21 MPa. The progressive increase of nanofiller content has led to enhanced polarization (11 μC/cm2), soft ferromagnetic properties, and enhanced ME coupling of 59 mV/cm-Oe due to switchable magnetostriction (λ11 = −18 ppm and dλ11/d = −22 × 10−9 Oe−1) at lower saturation field of 1.2 kOe. The ME sensitivity was found to be more than two-folds enhanced compared to solution-cast films making them prospective self-biased flexible devices for wearable electronics. Simultaneously, enhanced change of magnetization (19.6 %) under electric field was obtained. Detailed energy storage characteristics confirm that the nanofiller inclusion up to 7.12 vol% effectively improved the recoverable energy storage density (21.2 J/cm3) with an efficiency of 67 %. The experimental and simulation results corroborate a significantly improved breakdown strength of 617 kV/mm with reliable performance. Thus, careful processing provides viable polymer dielectrics with beneficial storage characteristics.