  Nebular emission lines are powerful diagnostics for the physical processes at
play in galaxy formation and evolution. Moreover, emission-line galaxies (ELGs)
are one of the main targets of current and forthcoming spectroscopic
cosmological surveys. We investigate the contributions to the line luminosity
functions (LFs) of different galaxy populations in the local Universe,
providing a benchmark for future surveys of earlier cosmic epochs. The large
statistics of the observations from the SDSS DR7 Main galaxy sample and the
MPA-JHU spectral catalogue enabled us to precisely measure the H$\alpha$,
H$\beta$, [OII], [OIII], and, for the first time, the [NII], and [SII]
emission-line LFs over ~2.4 Gyrs in the low-z Universe, 0.02<z<0.22. We present
a generalized 1/Vmax LF estimator capable of simultaneously correcting for
spectroscopic, r-band magnitude, and emission-line incompleteness. We studied
the contribution to the LF of different types of ELGs classified using two
methods: (i) the value of the specific star formation rate (sSFR), and (ii) the
line ratios on the Baldwin-Phillips-Terlevich (BPT) and the WHAN (i.e.,
H$\alpha$ equivalent width versus the [NII]/H$\alpha$ line ratio) diagrams. The
ELGs in our sample are mostly star forming, with 84 per cent having
sSFR>10$^{-11}$/yr. When classifying ELGs using the BPT+WHAN diagrams, we find
that 63.3 per cent are star forming, only 0.03 are passively evolving, and 1.3
have nuclear activity (Seyfert). The rest are low-ionization narrow
emission-line regions (LINERs) and composite ELGs. We found that a Saunders
function is the most appropriate to describe all of the emission-line LFs, both
observed and dust-extinction-corrected. They are dominated by star-forming
regions, except for the bright end of the [OIII] and [NII] LFs (i.e.
L[NII]>10$^{42}$ erg/s, L[OIII]>10$^{43}$ erg/s), where the contribution of
Seyfert galaxies is not negligible.
