The levels of $^{158}\mathrm{Dy}$ populated in the decay of 11-min $^{158}\mathrm{Ho}^{g}$ and 28-min $^{158}\mathrm{Ho}^{m}$ in equilibrium with 2.3-h $^{158}\mathrm{Er}$ have been studied using singles Ge(Li) detectors, a Compton-suppression spectrometer and a Ge(Li)-Ge(Li) coincidence spectrometer. We firmly establish $K=0$ one-phonon $\ensuremath{\beta}$-vibrational, $K=2$ one-phonon $\ensuremath{\gamma}$-vibrational, $K=2$ two-phonon ($\ensuremath{\beta}+\ensuremath{\gamma}$)-vibrational, and $K=4$ two-quasineutron bands with new $\ensuremath{\gamma}$-ray singles, coincidence, and multipolarity evidence. Members of the $K=0, 1, 2, \mathrm{and} 3$ octupole vibrational bands are identified and compared to theoretical calculations. One-phonon octupole vibrational bands are proposed with the following assignments ${I}^{\ensuremath{\pi}}$(keV): $K=0$: ${1}^{\ensuremath{-}}$(1608.0), ${3}^{\ensuremath{-}}$(1671.8), ${5}^{\ensuremath{-}}$(1818.7); $K=1$: ${1}^{\ensuremath{-}}$(1441.7), ${2}^{\ensuremath{-}}$(1501.1), ${3}^{\ensuremath{-}}$(1513.6), ${4}^{\ensuremath{-}}$(1618.4), ${5}^{\ensuremath{-}}$(1634.5); $K=2$: ${2}^{\ensuremath{-}}$(1371.7), ${3}^{\ensuremath{-}}$(1397.2), ${4}^{\ensuremath{-}}$(1518.5), ${5}^{\ensuremath{-}}$(1528.1); and $K=3$: ${3}^{\ensuremath{-}}$(2409.6). A limiting value $\ensuremath{\rho}\ensuremath{\ge}0.09$ has been measured for the monopole matrix element of the 990.6-keV $\ensuremath{\beta}$ vibration and a new low-lying ${0}^{+}$ state is reported at 1710.2 keV which may have collective character.RADIOACTIVITY $^{158}\mathrm{Ho}$ [from $^{149}\mathrm{Sm}$ ($^{12}\mathrm{C}$, $3n$)(2.3-h, EC, ${\ensuremath{\beta}}^{+}$) $^{158}\mathrm{Ho}$]; measured $E\ensuremath{\gamma}$, $I\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\gamma}$ coin; deduced $log\mathrm{ft}$. $^{158}\mathrm{Dy}$ deduced levels, $J$, $\ensuremath{\pi}$, ${\ensuremath{\alpha}}_{K}$, $\ensuremath{\gamma}$ multipolarities. Ge(Li) detectors, enriched targets.