Context. Multi-wavelength studies of galaxies and galactic nuclei allow us to build a relatively more complete picture of the interstellar medium (ISM), especially in the dusty regions of starburst galaxies. An understanding of the physical processes in nearby galaxies can assist in the study of more distant sources at higher redshifts that cannot be resolved.Aims. We aimed to use observations presented in the first part of this series of papers to model the physical conditions of the ISM in the nuclear region of NGC 253, in order to obtain primary parameters such as gas densities and metallicities. From the model we created, we further calculated secondary parameters, such as gas masses of the different phases, and estimated the fraction of [C II]158 mu m from the different phases, which allowed us to probe the nuclear star formation rate.Methods. To compare theory with our observations we used MULTIGRIS, a probabilistic tool that determines probabilities for certain ISM parameters from a grid of Cloudy models together with a set of spectroscopic lines.Results. We find that the hypothetical active galactic nucleus within NGC 253 has only a minor impact, compared to the starburst, on the heating of the ISM, as probed by the observed lines. We characterise the ISM and obtain parameters such as a solar metallicity, a mean density of similar to 230 cm(-3), an ionisation parameter of log U approximate to -3, and an age of the nuclear cluster of similar to 2 Myr. Furthermore, we estimate the masses of the ionised (3.8 x 10(6) M-circle dot), neutral atomic (9.1 x 10(6) M-circle dot), and molecular (2.0 x 10(8) M-circle dot) gas phases as well as the dust mass (1.8 x 10(6) M-circle dot) in the nucleus of NGC 253.