JHKLM (1-5 micron) imaging of a sample of Seyfert (Sy) 2 galaxies is presented. We confirm that the 1-2.2 micron nuclear continuum of some Sy 2s is dominated by stellar emission, whereas the continuum emission at longer wavelengths (3-5 micron) is almost entirely non-stellar in origin. The IR non-stellar spectral energy distributions (SED) (up to 15 micron) of Sy galaxies show a variety of shapes, and they are well reproduced with the tapered disk models of Efstathiou & Rowan-Robinson (1995). We have used two models, one including an optically thin cone component and a coneless model. Although our modelling of the SEDs does not allow us to favor either model to account for all the observed SEDs, we find that the viewing angle towards the central source is well constrained by both models. We have also investigated non-stellar color-color diagrams. The colors of the Sy galaxies with viewing angles theta < 30 degree are better reproduced with the cone model. These diagrams provide a good means to separate Sy 2s with moderate obscuration (A_V < 20 mag, from hard X-ray observations) from those with high obscuration. The ground-based 4.8 micron and ISO 9.6 micron luminosities are well correlated with the hard X-ray luminosities of Sy 1s and 2s. These continuum emissions appear as a good indicator of the AGN luminosity, at least in the cases of hard X-ray Compton-thin Sy galaxies. We finally stress the finding that some Compton thick galaxies show bright non-stellar emission at 5 micron. This suggests that the near-IR emission in Sys is produced in an extended component illuminated by the central source, that is more visible from all viewing angles. We discuss possible implications of mid-IR surveys for the search of counterparts of highly obscured hard X-ray sources. (Abridged)