  We determine the model-independent component of the couplings of axions to
electroweak gauge bosons, induced by the minimal coupling to QCD inherent to
solving the strong CP problem. The case of the invisible QCD axion is developed
first, and the impact on $W$ and $Z$ axion couplings is discussed. The analysis
is extended next to the generic framework of heavy true axions and low axion
scales, corresponding to scenarios with enlarged confining sector. The mass
dependence of the coupling of heavy axions to photons, $W$ and $Z$ bosons is
determined. Furthermore, we perform a two-coupling-at-a-time phenomenological
study where the gluonic coupling together with individual gauge boson couplings
are considered. In this way, the regions excluded by experimental data for the
axion-$WW$, axion-$ZZ$ and axion-$Z\gamma$ couplings are determined and
analyzed together with the usual photonic ones. The phenomenological results
apply as well to ALPs which have anomalous couplings to both QCD and the
electroweak bosons.
