The coupling of ferromagnetic and ferroelectric materials has sparked great interest in the field of spintronics due to nonvolatile electrical magnetic control. In this work, we propose two-dimensional multiferroic ${\text{MnSe}}_{2}/{\text{In}}_{2}{\text{Se}}_{3}$ van der Waals (vdW) heterostructure to investigate the magnetoelectric coupling. The electronic structure, magnetic anisotropy, magnetic phase transition, and transport properties were investigated by employing the first-principles calculations in combination with the nonequilibrium Green's function method. The results reveal that polarization reversal not only can effectively tune the Schottky-to-Ohmic contact but also reorients the magnetic easy axis. In addition, Curie temperature (${T}_{c}$) was predicted based on the Heisenberg model and Monte Carlo simulations, and the competition between interfacial charge injection and lattice mismatch determines the ${T}_{c}$ of ${\text{MnSe}}_{2}/{\text{In}}_{2}{\text{Se}}_{3}$ heterostructure. Furthermore, we constructed the vdW ${\text{MnSe}}_{2}/{\text{In}}_{2}{\text{Se}}_{3}$-based magnetic-tunnel-junction and ferroelectric-tunnel-junction nanodevice, which exhibits high tunneling magnetoresistance of up to $1.805\ifmmode\times\else\texttimes\fi{}{10}^{3}\mathrm{%}$ and a spin-filter efficiency of up to 98.5%. Our findings demonstrate the significant potentials of multiferroic ${\text{MnSe}}_{2}/{\text{In}}_{2}{\text{Se}}_{3}$ vdW heterostructures in designing a next-generation spintronic and nonvolatile memory device.