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 $241.50pm0.05$ day period; a tertiary companion orbits that inner pair with a $4218pm50$ 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.
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