Resonantly damped fast kink quasi-modes are computed in fully resistive magnetohydrodynamics (MHD) for two-dimensional equilibrium models. The equilibrium model is a straight cylindrically symmetric flux tube with a plasma density that is non-uniform both across and along the loop. The non-uniform layer across the loop is not restricted to be thin, but its thickness can reach values up to the loop diameter. Our results indicate that the period and damping of coronal loop oscillations mainly depend on the density contrast and the inhomogeneity length-scale and are independent of the details of longitudinal stratification, depending on the weighted mean density, weighted with the wave energy. For fully non-uniform loops, quasi-modes can interact with resistive Alfvén eigenmodes leading to avoided crossings and gaps in the complex frequency plane. The present study extends previous studies on coronal loop oscillations in one-dimensional equilibrium models with thick boundary layers and in equilibria with longitudinally stratified loops under the thin boundary approximation, and allow for a better comparison between observations and theory raising the prospect of coronal seismology using the time damping of coronal loop oscillations.