Based on the extended Su-Schrieffer-Heeger model and the nonadiabatic-dynamics method, we investigate the field-dependent polaron dynamics as well as its effect on the organic spin Hall effect (SHE) in three coupled organic chains with spin-orbit coupling. The results demonstrate a steplike transition of the polaron velocity with the increase of field strength, caused by the decoupling of the acoustic and optical deformations, and a dissociation of the polaron at stronger fields. The critical fields for decoupling and dissociation are much smaller than those reported for single-chain polymers due to the interchain coupling. Importantly, a distinct field dependence of the SHE and the charge-spin conversion efficiency is revealed. For subsonic polaron transport, the amplitude of the SHE increases with the field strength, whereas it shows a nonmonotonic field dependence in the supersonic regime. A large SHE is obtained even when the polaron is dissociated at strong fields. In contrast, the largest charge-spin conversion efficiency is found for the weak fields in the subsonic regime, caused by the small polaron velocity. The mechanism is analyzed in terms of the change of lattice distortions including both breathers and polaron distortions, which modulate the skew scattering from lattice distortions as well as the interchain spin transfer, and thus modify the SHE. In addition, the oscillations of the SHE in the various regimes are investigated by spectral analysis. This work sheds light on the microscopic mechanism of the electric-field effect on the SHE in organic polymers, which provides guidance for the pursuit of a strong SHE or a large charge-spin conversion efficiency via field manipulation.