We present subarcsec near-infrared 1.5-2.5 μm moderate resolution long-slit spectra of eight nearby Seyfert galaxies (z < 0.01), both parallel to the ionization cone and perpendicular to it. These spectra complement similar data on six Seyferts, presented in Reunanen, Kotilainen & Prieto, and are used to study the spatial extent of the line emission, the integrated masses of excited H2 and the excitation mechanisms of interstellar gas. Large concentrations of molecular gas (H2) are present in the nucleus regardless of the Seyfert type. The spatial extent of the H2 emission is larger perpendicular to the cone than parallel to it in 6/8 (75 per cent) galaxies, in agreement with the unified models of active galactic nuclei. The full width at half maximum (FWHM) sizes of the nuclear H2 emission range from <20 to ~300 pc, and are larger than the predicted sizes for molecular torus (1-100 pc). Thus the emission probably arises from the material surrounding the torus rather than directly from the torus. Broad Brγ was detected in nearly half of the optically classified Seyfert 2 galaxies, including two objects with no evidence for a hidden polarized broad line region. This high detection rate stresses the importance of extinction effects as the main cause for the Seyfert dichotomy. Brγ and [Fe II] correlate both spatially and kinematically. Nuclear [Fe II] emission is generally blueshifted which, together with the high Brγ/[Fe II] ratios, suggests shocks as the dominant excitation mechanism in Seyfert galaxies. Bright coronal emission lines [SiVI] and [Si VII] are common in Seyferts, as they are detected in ~60 per cent of the galaxies. In three galaxies the coronal lines are extended only in the direction parallel to the cone. This could be explained by a strongly collimated radiation field or, most plausibly, by shock excitation due to the jet or superwind interacting with the interstellar medium.