  Heavy sterile neutrinos with masses below $M_W$ can induce trilepton events
at the 14 TeV LHC through purely leptonic $W$ decays of $W^\pm \to e^\pm e^\pm
\mu^\mp \nu$ and $\mu^\pm \mu^\pm e^\mp \nu$ where the heavy neutrino will be
in an intermediate state on its mass shell. Discovery and exclusion limits for
the heavy neutrinos are found using both Cut-and-Count (CC) and a Multi-Variate
Analysis (MVA) methods in this study. We also show that it is possible to
discriminate between a Dirac and a Majorana heavy neutrino, even when lepton
number conservation cannot be directly tested due to unobservability of the
final state neutrino. This discrimination is done by exploiting a combined set
of kinematic observables that differ between the Majorana vs. Dirac cases. We
find that the MVA method can greatly enhance the discovering and discrimination
limits in comparison with the CC method. For a 14-TeV $pp$ collider with
integrated luminosity of 3000 ${\rm fb}^{-1}$, sterile neutrinos can be found
with 5$\sigma$ significance if heavy-to-light neutrino mixings $|U_{Ne}|^2 \sim
|U_{N\mu}|^2 \sim 10^{-6}$, while the Majorana vs. Dirac type can be
distinguished if $|U_{Ne}|^2 \sim |U_{N\mu}|^2 \sim 10^{-5}$ or even
$|U_{N\ell}|^2\sim 10^{-6}$ if one of the mixing elements is at least an order
of magnitude smaller than the other.
