The paper studies novel solitary waves with the (3 + 1)-dimensional nonlinear Schrödinger equation in birefringent fibers having a white noise effect. This model is reported in this paper for the first time, guaranteeing that the analysis and results are novel and original. To investigate this model, we implement two techniques, namely, the projective Riccati equation method and the enhanced direct algebraic method. The obtained solutions are bright solitons, dark solitons, singular solitons, and straddled solitons. Besides these solitons, Jacobi and Weierstrass elliptic solutions are also obtained. These findings expand our understanding of nonlinear wave propagation in birefringent fibers under the influence of white noise and introduce new mathematical methods for solving complex nonlinear differential equations.