New van der Waals (vdW) heterostructures obtained by stacking monolayers of recently synthesized graphenylene (Gr) and two-dimensional 1H-MoX2 (X = S, Te, and Se) are proposed and analyzed using ab initio calculations. These heterostructures are stable under normal conditions and have unique crystalline lattices. The study of electronic properties shows that the proposed materials are direct-gap semiconductors with a narrow band gap, which can be controlled by in-plane tensile strain or a transverse electric field. The considered vdW heterostructures demonstrate the transition of band alignments between types I, II and III, when in-plane stress or a transverse electric field is applied, and hold great potential for creating multifunctional devices for stretched electronics. Computations based on the non-equilibrium Green's function method indicate a high rectification factor of the order of 103-104 for a diode based on the Gr/MoS2 vdW junction. The studied structures exhibit broad optical absorption across the entire visible range and represent a promising material for optoelectronic applications.