By utilizing symmetry analysis and electronic structure calculations, we investigated the low-temperature orthorhombic phase of Ag$_{2}$Se in ${\cal SG}$~17. In addition to the discovery of a nodal plane at $k_{z}=\pi$ protected by the joint operation of time-reversal (${\cal T}$) and the 2-fold screw rotation $S_{2z}$, we found 24 Weyl points mainly residing at the $k_{y}=0$ plane with notable Fermi arc and large quasiparticle interference pattern (QPI). Due to the absence of mirror symmetry, a pair of Weyl points with opposite chirality reside at different binding energies, which makes this system an excellent material candidate for realizing the novel chiral anomaly related phenomenon, such as the quantized circular photogalvanic and the chiral magnetic effects. Furthermore, we also reveal the striking spin textures at $k_{z}=\pi$ plane which demonstrates, in a large region of the surface Brillouin Zone, a direction-selective spin polarization, which has a strong implication to spintronic applications.