Disorders such as impurities or defects inevitably induce complex scatterings in realistic material systems. As a result, we need transport theories dealing with these disorder scatterings to compute electronic transports. The self-consistent Born approximation (SCBA) is an effective field-theoretical approach for weak disorders by incorporating scatterings into both self-energy and vertex corrections self-consistently. However, previous SCBA theory relies on isotropic assumptions and lacks a systematic symmetry analysis for anisotropic systems. He we develop a symmetry-constrained SCBA (SCSCBA) framework for disordered semi-Dirac fermion systems by combining joint space symmetries consisting of both momentum and pseudospin space with intrinsic discrete symmetries including particle-hole symmetry (PHS), time-reversal symmetry (TRS) and chiral symmetry(CS). Through symmetry constraints we reduce self-energy, single current-vertex and double current-vertex tensors into a few scalar algebraic equations, thereby greatly simplifying self-consistent calculations on transport properties. Applying SCSCBA, we systematically investigate the self-energy, band renormalization, vertex corrections, longitudinal conductivity, and Hall conductivity of disordered semi-Dirac fermion systems. We find that, (i) both the real and imaginary parts of the self-energy preserve the PHS, and the increased disorder strength drives the initial semi-Dirac metallic phase into two-node semimetals through the Lifshitz transition; (ii) For longitudinal conductivity, along the linear-dispersion direction there exists a robust minimum close to 4e^2/\pi h near zero energy reflecting the underlying Klein-tunneling nature of Dirac fermions, whereas the conductivity along the quadratic-dispersion direction vanishes at zero energy, manifesting a remarkable anisotropy; (iii) The weak-field Hall conductivity exhibts an odd function feature with energy, and the Fermi-surface contribution plays the dominant role in the Hall response, compared with the Fermi-sea contribution; (iv) Away from zero energy, both longitudinal and Hall conductivities are significantly suppressed by disorders. The suggested SCSCBA perspective can also be extended into other anisotropic systems.