Natural fiber composites (NFC) are eco-friendly alternatives to synthetic polymers. However, some intrinsic natural fillers’ properties hinder their widespread implementation as reinforcement in polymeric matrices and require further investigation. In the scope of this study, the thermal, rheologic, mechanical (tension and flexural modes), and morphological properties, as well as the water absorption and dimensional stability of the NF polypropylene (PP)-based injection molded composites reinforced with rice husk (rh) and olive pits (op) of 20 wt.% and 30% wt.%, respectively, were investigated. The results suggest that the higher content of the rice husk and olive pits led to a similar reduction in the melt flow index (MFI), independent of the additive type compared to virgin polypropylene (PPv). The melting and crystallization temperatures of the PPrh and PPop composites did not change with statistical significance. The composites are stiffer than the PP matrix by up to 49% and possess higher mechanical strength in the tension mode at the expense of decreased ductility. PPrh and PPop have a superior flexural modulus in the bending mode, while the flexural strength improvement was accomplished for the PP30%rh. The influence of the fibers’ distribution in the bulk of the parts on their mechanical performance was confirmed based on a non-localized morphology evaluation, which constitutes a novelty of the presented research. The dimensional stability of the composites was improved as the linear shrinkage in the flow direction was decreased by 49% for PPrh and 30% for PPop, positively correlating with an increase in the filler content and stiffness. PPop was less susceptible to water sorption than PPrh due to fibers’ composition and larger surface-to-area volume ratios.