We analyse spectral properties of 1671 galaxies from the Stromlo-APM Survey, selected to have 15 less than or equal to b(J) less than or equal to 17.15 and having a mean redshift z = 0.05. This is a representative local sample of field galaxies, so the global properties of the galaxy population provide a comparative point for analysis of more distant surveys. We measure H alpha, [O II] lambda 3727, [S II] lambda lambda 6716, 6731, [N II] lambda 6583 and [O I] lambda 6300 equivalent widths and the D-4000 break index. The 5-Angstrom-resolution spectra use an 8-arcsec slit, which typically covers 40-50 per cent of the galaxy area. We find no evidence for systematic trends depending on the fraction of galaxy covered by the slit, and further analysis suggests that our spectra are representative of integrated galaxy spectra. We classify spectra according to their H alpha emission, which is closely related to massive star formation. Overall we find that 61 per cent of galaxies are H alpha emitters with rest-frame equivalent widths EW(H alpha) greater than or similar to 2 Angstrom. The emission-line galaxy (ELG) fraction is smaller than seen in the Canada-France Redshift Survey (CFRS) at z = 0.2, and is consistent with a rapid evolution of H alpha luminosity density. The ELG fraction and EW(H alpha) increase at fainter absolute magnitudes, smaller projected area and smaller D-4000. In the local Universe, faint, small galaxies are dominated by star formation activity, while bright, large galaxies are more quiescent. This picture of the local Universe is quite different from that of the distant one; bright galaxies appear to show rapidly increasing activity as one moves further back in time. We find that the ratio [N II] lambda 6583/H alpha is anticorrelated with EW(H alpha), and that the value of 0.5 commonly used to remove the [N II] contribution from blended H alpha + [N II] lambda lambda 6548, 6583 applies only for samples with an EW distribution similar to that seen at low redshift. We show that the [O II], [N II], [S II] and H alpha EWs are correlated, but with large dispersions (similar to 50 per cent) owing to the diversity of galaxy contents sampled. Our [O II]-H alpha relation is similar to the one derived by Kennicutt, but is 10 per cent higher at 1 sigma significance. We show that this relation is not valid for distant, strong [O II] emitters with blue colours, which are more numerous than locally. This relation would overestimate the individual star formation rate by similar to 50 per cent for these kinds of galaxies. We find that, on average, luminous blue ELGs are likely to be enhanced in nitrogen abundance. This suggests that in faint, low-mass, late-type ELGs nitrogen is a primary element, whereas in brighter, more massive galaxies nitrogen comes from a secondary source. We also find that 4 per cent of early-type galaxies show star formation activity; this fraction seems to increase at higher redshifts.