We present NuSTAR hard X-ray (3-79 keV) observations of three Type 2 quasars at z ~ 0.4-0.5, optically selected from the Sloan Digital Sky Survey (SDSS). Although the quasars show evidence for being heavily obscured Compton-thick systems on the basis of the 2-10 keV to [OIII] luminosity ratio and multiwavelength diagnostics, their X-ray absorbing column densities (N_H) are poorly known. In this analysis: (1) we study X-ray emission at >10 keV, where X-rays from the central black hole are relatively unabsorbed, in order to better constrain N_H; (2) we further characterize the physical properties of the sources through broad-band near-UV to mid-IR spectral energy distribution (SED) analyses. One of the quasars is detected with NuSTAR at >8 keV with a no-source probability of <0.1%, and its X-ray band ratio suggests near Compton-thick absorption with N_H gtrsim 5 x 10^23 cm^-2. The other two quasars are undetected, and have low X-ray to mid-IR luminosity ratios in both the low energy (2-10 keV) and high energy (10-40 keV) X-ray regimes that are consistent with extreme, Compton-thick absorption (N_H gtrsim 10^24 cm^-2). We find that for quasars at z ~ 0.5, NuSTAR provides a significant improvement compared to lower energy (<10 keV) Chandra and XMM-Newton observations alone, as higher column densities can now be directly constrained.