Beryllium polynitrides, (BeN4) is a novel layered material, which has been most recently fabricated under high pressure (Phys. Rev. Lett. 126 (2021), 175501). As a new class of two-dimensional (2D) materials, in this work, we conduct first-principles calculations to examine the stability and explore the electronic nature of MN4 (M = Be, Mg, Ir, Rh, Ni, Cu, Au, Pd, and Pt) monolayers. Acquired results confirm the dynamical and thermal stability of BeN4, MgN4, IrN4, PtN4, and RhN4 monolayers. Interestingly, BeN4 and MgN4 monolayers are found to show anisotropic Dirac cones in their electronic structure. Although PtN4 monolayer is predicted to be a narrow bandgap semiconductor, IrN4 and RhN4 monolayers are found to be metallic systems. We also elaborately explore the effects of the number of atomic layers on the electronic features of BeN4 nanosheets, which reveal highly appealing physics. Our results highlight that BeN4 nanosheet yield ultrahigh elastic modulus and mechanical strength, outperforming all other carbon-free 2D materials. Notably, RhN4 nanosheet is predicted to yield high capacities of 562, 450, and 900 mAh/g for Li, Na, and Ca ions storages, respectively. This study provides a comprehensive understanding of the intrinsic properties of MN4 nanosheets and highlights their outstanding physics.