Resonant transport regimes in tokamaks with nonaxisymmetric perturbations are treated by the application of Hamiltonian perturbation theory in action-angle variables. The main advantages of this method are the independence from assumptions on geometry such as the large-aspect-ratio limit and its extensibility to non-linear regimes. In the context of this problem, weakly non-linear theory is applied to go beyond the quasilinear limit and allow for a physically consistent transition between limiting cases. The initial part introduces methods for studying resonant effects in a perturbed Hamiltonian system subject to collisional effects. The approach is then applied to the specific problem of resonant transport regimes in a non-axisymmetrically perturbed tokamak plasma. Results from computations confirm the significance of contributions from those regimes to neoclassical toroidal viscous torque in medium-sized tokamaks with magnetic perturbations from coils installed for the control of edge-localized modes. The major practical features of this work relevant for quantitative evaluation of toroidal torque are complete geometry, consideration of magnetic drift, magnetic shear and the transition region between quasilinear and non-linear regimes.