The quasi-one-dimensional (Q1D) molecular conductors (DIETSe)(2)MCl4 [M = Fe, Ga] undergo a spin density wave (SDW) transition below 12 K. The SDW ground state is suppressed by applying high pressure, recovering the Q1D Fermi surface which is confirmed by the appearance of Lebed resonance in the angle-dependent magnetoresistance (MR). Above the critical pressure of SDW, MR shows kink structures at high magnetic fields, reminiscent of field-induced spin density wave (FISDW) transition in both salts. The pi-d hybrid (DIETSe)(2)FeCl4 also exhibits an antiferromagnetic (AF) transition of d-electron spins at 2.5 K, below which the spin-flop-induced positive large MR are observed. The change in the interlayer MR reaches 130% at 10.5 kbar. The resistance anomalies associated with spin flop are also observed in the angle-dependent MR at low magnetic fields below 5 T, associated with clear hysteresis. A polar plot of these anomalies reveals the presence of hidden spin canting. Two magnetic easy axes of d-electron spins are found to be tilted +/- 16 degrees from the b axis towards the c axis. The interplay between the SDW instability of Q1D pi electrons and the local moments of AF d-electron spins is considered as the origin of the anomalous transport behaviors. DOI: 10.1103/PhysRevB.87.085117