We present STAR measurements of strange hadron ($mathrm{K}^{0}_{mathrm S}$, $Lambda$, $overline{Lambda}$, $Xi^-$, $overline{Xi}^+$, $Omega^-$, $overline{Omega}^+$, and $phi$) production at mid-rapidity ($|y| < 0.5$) in Au+Au collisions at $sqrt{s_{_{mathrm{NN}}}}$ = 7.7 - 39 GeV from the Beam Energy Scan Program at the Relativistic Heavy Ion Collider (RHIC). Transverse momentum spectra, averaged transverse mass, and the overall integrated yields of these strange hadrons are presented versus the centrality and collision energy. Antibaryon-to-baryon ratios ($overline{Lambda}$/$Lambda$, $overline{Xi}^+$/$Xi^-$, $overline{Omega}^+$/$Omega^-$) are presented as well, and used to test a thermal statistical model and to extract the temperature normalized strangeness and baryon chemical potentials at hadronic freeze-out ($mu_{B}/T_{rm ch}$ and $mu_{S}/T_{rm ch}$) in central collisions. Strange baryon-to-pion ratios are compared to various model predictions in central collisions for all energies. The nuclear modification factors ($R_{textrm{CP}}$) and antibaryon-to-meson ratios as a function of transverse momentum are presented for all collision energies. The $mathrm{K}^{0}_{mathrm S}$ $R_{textrm{CP}}$ shows no suppression for $p_{rm T}$ up to 3.5 $mathrm{GeV} / c$ at energies of 7.7 and 11.5 GeV. The $overline{Lambda}$/$mathrm{K}^{0}_{mathrm S}$ ratio also shows baryon-to-meson enhancement at intermediate $p_{rm T}$ ($approx$2.5 $mathrm{GeV} / c$) in central collisions at energies above 19.6 GeV. Both observations suggest that there is likely a change of the underlying strange quark dynamics at collision energies below 19.6 GeV.
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