Cross sections are presented for the inclusive photoproduction of ${K}_{S}^{0}$, \ensuremath{\Lambda}, \ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{}, ${\ensuremath{\Xi}}^{\mathrm{\ensuremath{-}}}$, \ensuremath{\Xi}\ifmmode\bar\else\textasciimacron\fi{}${\mathrm{}}^{\mathrm{\ensuremath{-}}}$, ${\ensuremath{\Sigma}}^{0}$, and ${\ensuremath{\Sigma}}^{\mathrm{*}\ifmmode\pm\else\textpm\fi{}}$(1385) at 20 GeV. An upper limit to ${\ensuremath{\Omega}}^{\mathrm{\ensuremath{-}}}$ production is also given. The data come from 284 000 hadronic events photoproduced in the SLAC 1-m hydrogen-bubble-chamber hybrid facility exposed to a nearly monochromatic, polarized 20-GeV backscattered photon beam. A comparison of the ${K}_{S}^{0}$, \ensuremath{\Lambda}, \ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{}, and ${\ensuremath{\Xi}}^{\mathrm{\ensuremath{-}}}$ rates per inelastic event to ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$p data show that \ensuremath{\gamma}p rates are consistent with being higher than the ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$p rates, providing evidence of an ss\ifmmode\bar\else\textasciimacron\fi{} component of the photon. The pair cross sections for ${K}_{S}^{0}$${K}_{S}^{0}$, ${K}_{S}^{0}$\ensuremath{\Lambda}, ${K}_{S}^{o}$\ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{}, and \ensuremath{\Lambda}\ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{} are presented. The ${x}_{F}$ distributions of the \ensuremath{\Lambda}, \ensuremath{\Lambda}\ifmmode\bar\else\textasciimacron\fi{}, and ${\ensuremath{\Xi}}^{\mathrm{\ensuremath{-}}}$ are compared to a quark-diquark fusion model, giving information on strange-baryon photoproduction mechanisms.