Most recently, N-graphdiyne two-dimensional (2D) nanomaterials were successfully experimentally realized at the gas/liquid and liquid/liquid interfaces. We accordingly conducted density functional theory (DFT) and molecular dynamics simulations to explore the mechanical/failure, thermal conductivity and stability, electronic and optical properties of three N-graphdiyne nanomembranes. Our DFT results of uniaxial tensile simulations reveal that these monolayers can yield remarkably high stretchability or tensile strength depending on the atomic structure and loading direction. Studied N-graphdiyne nanomembranes were found to exhibit semiconducting electronic character, with band-gap values ranging from 0.98 eV to 3.33 eV, based on the HSE06 estimations. The first absorption peak suggests that these 2D structures can absorb visible, IR and NIR light. Ab initio molecular dynamics results reveal that N-graphdiyne 2D structures can withstand at high temperatures, like 2000 K. Thermal conductivities of suspended single-layer N-graphdiyne sheets were predicted to be almost temperature independent and about three orders of magnitude smaller than that of the graphene. The comprehensive insight provided by this work highlights the outstanding physics of N-graphdiyne 2D nanomaterials, and suggest them as highly promising candidates for the design of novel stretchable nanodevices.