  We study the contribution of massive dominantly sterile neutrinos, $N$, to
the Lepton Number and Lepton Flavor Violating semileptonic decays of $\tau$ and
$B, D, K$-mesons. We focus on special domains of sterile neutrino masses
$m_{N}$ where it is close to its mass-shell. This leads to an enormous resonant
enhancement of the decay rates of these processes. This allows us to derive
stringent limits on the sterile neutrino mass $m_{N}$ and its mixing $U_{\alpha
N}$ with active flavors. We apply a joint analysis of the existing experimental
bounds on the decay rates of the studied processes. In contrast to other
approaches in the literature our limits are free from ad hoc assumptions on the
relative size of the sterile neutrino mixing parameters. We analyze the impact
of this sort of assumptions on the extraction of the limits on $m_{N}$ and
$U_{\alpha N}$, and discuss the effect of finite detector size. Special
attention was paid to the limits on meson decays with $e^{\pm}e^{\pm}$ in final
state, derived from non-observation of $0\nu\beta\beta$-decay. We point out
that observation of these decays may, in particular, shed light on the Majorana
phases of the neutrino mixing matrix.
