A comprehensive investigation was carried out on graphyne/graphyne (Gyne/Gyne), graphyne-like BN/graphyne-like BN (BNyne/BNyne) and graphyne/graphyne-like BN (Gyne/BNyne) bilayer structures using van der Waals (vdW)-corrected density functional theory. These bilayers exhibited distinct stacking-dependent characteristics in their ground state electronic structure and also had different responses to external strain and a vertical electric field. For the Gyne/Gyne and Gyne/BNyne bilayers, the application of biaxial tensile strain led to an increase in the band gap, while the application of biaxial compressive strain in addition to uniaxial strain, either under tension or compression, induced a reduction in the band gap. However, in the case of the BNyne/BNyne bilayer, the application of biaxial tensile strain led to a decrease in the band gap, but an increase in the band gap occurred under biaxial compressive strain, which could be explained by a change in the ionic nature of the B-N bonds. Under a vertical electric field, the band gaps of the homo-bilayers (Gyne/Gyne and BNyne/BNyne) decreased and were symmetrical. However, the hetero-bilayer (Gyne/BNyne) exhibited a decreased band gap under a positive electric field, but an almost constant band gap under a negative electric field. The physical origin of the band gap variation under an electric field was unraveled using energy-band theory. Our findings pave the way for experimental research and provide valuable insight into two-dimensional vdW layered structures for use in next generation flexible nanoelectronics and optoelectronic devices.