This study investigated the mechanical, physical, and thermal properties of three-layer particleboards produced from annual plant straws and three polymers: polypropylene (PP), high-density polyethylene (HDPE), and polylactic acid (PLA). The rape straw (Brassica napusL. var. Napus) was used as an internal layer, while rye (SecaleL.) or triticale (TriticosecaleWitt.) was applied as an external layer in the obtained particleboards. The boards were tested for their density, thickness swelling, static bending strength, modulus of elasticity, and thermal degradation characteristics. Moreover, the changes in the structure of composites were determined by infrared spectroscopy. Among the straw-based boards with the addition of tested polymers, satisfactory properties were obtained mainly using HDPE. In turn, the straw-based composites with PP were characterized by moderate properties, while PLA-containing boards did not show clearly favorable properties either in terms of the mechanical or physical features. The properties of straw–polymer boards produced based on triticale straw were slightly better than those of the rye-based boards, probably due to the geometry of the strands, which was more favorable for triticale straw. The obtained results indicated that annual plant fibers, mainly triticale, can be used as wood substitutes for the production of biocomposites. Moreover, the addition of polymers allows for the use of the obtained boards in conditions of increased humidity.