The generation and control of entanglement in a quantum mechanical system are critical elements of nearly all quantum applications. Molecular systems are promising candidates, with numerous degrees of freedom able to be targeted. However, knowledge of intersystem entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bimolecular system, we show that entanglement can be generated not only between the cavity and molecular system but also between molecules. This process also results in the generation of nonclassical states of light, providing potential pathways for harnessing entanglement in molecular systems.