The theories of hopping transport in quasi-one-dimensional disordered organic solids with Gaussian distribution of localized state energies are generalized to account for distant-neighbor transitions. The former theories predicted a resistivity temperature dependence of the form ln(rho)=C(sigma/kT)2, where C is a constant (C about 1) and sigma is the disorder parameter; we show that for distant-neighbor hopping, the coefficient C becomes a function of temperature C(T) and decreases with decreasing temperature. We obtain an analytic solution for the mobility taking account of second-nearest neighbor hopping; the onset of second-nearest neighbor hopping with decreasing temperature leads to a decrease of C(T) to the limiting value C=3/4. At lower temperatures, where the hopping range extends beyond second-nearest neighbors, C(T) is further decreased. The analytical results are in fair agreement with the results of Monte-Carlo simulation of one-dimensional variable-range hopping. We argue that for systems, where site size exceeds edge-to-edge separation between the neighboring sites, virtual-state-assisted second-nearest-neighbor transitions can enhance the role of distant-neighbor hopping.