  We present spatially and spectrally resolved Atacama Large
Millimeter/submillimeter Array (ALMA) observations of gas and dust orbiting the
pre-main sequence hierarchical triple star system GW Ori. A forward-modeling of
the ${}^{13}$CO and C${}^{18}$O $J$=2-1 transitions permits a measurement of
the total stellar mass in this system, $5.29 \pm 0.09\,M_\odot$, and the
circum-triple disk inclination, $137.6 \pm 2.0^\circ$. Optical spectra spanning
a 35 year period were used to derive new radial velocities and, coupled with a
spectroscopic disentangling technique, revealed that the A and B components of
GW Ori form a double-lined spectroscopic binary with a $241.50\pm0.05$ day
period; a tertiary companion orbits that inner pair with a $4218\pm50$ day
period. Combining the results from the ALMA data and the optical spectra with
three epochs of astrometry in the literature, we constrain the individual
stellar masses in the system ($M_\mathrm{A} \approx 2.7\,M_\odot$,
$M_\mathrm{B} \approx 1.7\,M_\odot$, $M_\mathrm{C} \approx 0.9\,M_\odot$) and
find strong evidence that at least one (and likely both) stellar orbital planes
are misaligned with the disk plane by as much as $45^\circ$. A $V$-band light
curve spanning 30 years reveals several new $\sim$30 day eclipse events
0.1-0.7~mag in depth and a 0.2 mag sinusoidal oscillation that is clearly
phased with the AB-C orbital period. Taken together, these features suggest
that the A-B pair may be partially obscured by material in the inner disk as
the pair approaches apoastron in the hierarchical orbit. Lastly, we conclude
that stellar evolutionary models are consistent with our measurements of the
masses and basic photospheric properties if the GW Ori system is $\sim$1 Myr
old.
