  The nuclear level densities of $^{118,119}$Sn and the $\gamma$-ray strength
functions of $^{116,118,119}$Sn below the neutron separation energy are
extracted with the Oslo method using the ($^3$He, \,$\alpha \gamma$) and
($^3$He,$^3$He$^\prime\gamma$) reactions. The level density function of
$^{119}$Sn displays step-like structures. The microcanonical entropies are
deduced from the level densities, and the single neutron entropy of $^{119}$Sn
is determined to be $(1.7 \pm 0.2)\,k_B$. Results from a combinatorial model
support the interpretation that some of the low-energy steps in the level
density function are caused by neutron pair-breaking. An enhancement in all the
$\gamma$-ray strength functions of $^{116-119}$Sn, compared to standard models
for radiative strength, is observed for the $\gamma$-ray energy region of
$\simeq (4 -11)$ MeV. These small resonances all have a centroid energy of
8.0(1) MeV and an integrated strength corresponding to $1.7(9)\%$ of the
classical Thomas-Reiche-Kuhn sum rule. The Sn resonances may be due to electric
dipole neutron skin oscillations or to an enhancement of the giant magnetic
dipole resonance.
