  Observed hot Jupiter (HJ) systems exhibit a wide range of stellar spin-orbit
misalignment angles. The origin of these HJs remains unclear. This paper
investigates the inward migration of giant planets due to Lidov-Kozai (LK)
oscillations induced by a distant (100-1000 AU) stellar companion. We conduct a
large population synthesis study, including the octupole gravitational
potential from the stellar companion, mutual precession of the host stellar
spin axis and planet orbital axis, tidal dissipation in the planet, and stellar
spin-down in the host star due to magnetic braking. We consider a range of
planet masses ($0.3-5\,M_J$) and initial semi-major axes ($1-5$AU), different
properties for the host star, and varying tidal dissipation strengths. The
fraction of systems that result in HJs depends on planet mass and stellar type,
with $f_{\rm HJ} = 1-4\%$ (depending on tidal dissipation strength) for
$M_p=1\,M_J$, and larger (up to $8\%$) for more massive planets. The production
efficiency of "hot Saturns" ($M_p=0.3M_J$) is much lower, because most
migrating planets are tidally disrupted. We find that the fraction of systems
that result in either HJ formation or tidal disruption, $f_{\rm mig} \simeq
11-14\%$ is roughly constant, having little variation with planet mass, stellar
type and tidal dissipation strength. This "universal" migration fraction can be
understood qualitatively from analytical migration criteria based on the
properties of octupole LK oscillations. The distribution of final HJ stellar
obliquities exhibits a complex dependence on the planet mass and stellar type.
For $M_p = (1-3)M_J$, the distribution is always bimodal, with peaks around
$30^{\circ}$ and $130^{\circ}$. The distribution for $5M_J$ planets depends on
host stellar type, with a preference for low obliquities for solar-type stars,
and higher obliquities for more massive ($1.4M_{\odot}$) stars.
