We present rigorous quantum calculations for low-temperature collisions of OH((2)Pi) molecules with He atoms in the presence of external electric and magnetic fields. We show that electric fields of less than 15 kV/cm call be used to enhance the probability for Stark relaxation in collisions of OH (F-1, J = 3/2, M = 3/2, f) molecules by 3 orders of magnitude. The inelastic cross sections display a pronounced resonance structure as a function of the electric field strength. We find that collisions of rotationally excited OH molecules become less sensitive to electric fields with increasing rotational excitation. The calculated total cross sections for He-4-OH are dominated by elastic scattering, increase monotonically with decreasing collision energy, and show no rapid variations near thresholds, at variance with recent experimental observations (Sawyer et al. Phys. Rev. Lett. 2008, 101, 203203).