The interesting and tunable properties of layered metal dichalcogenides heavily depend on their phase and layer stacking. Here, we show and explain how the layer stacking and physical properties of WSe2 are influenced by screw dislocations. A one-to-one correlation of atomic force microscopy and high- and low-frequency Raman spectroscopy of many dislocated WSe2 nanoplates reveals variations in the number and shapes of dislocation spirals and different layer stackings that are determined by the number, rotation, and location of the dislocations. Plates with triangular dislocation spirals form noncentrosymmetric stacking that gives rise to strong second-harmonic generation and enhanced photoluminescence, plates with hexagonal dislocation spirals form the bulk 2H layer stacking commonly observed, and plates containing mixed dislocation shapes have intermediate noncentrosymmetric stackings with mixed properties. Multiple dislocation cores and other complexities can lead to more complex stackings and properties. These previously unobserved properties and layer stackings in WSe2 will be interesting for spintronics and valleytronics.