This work presents an in-depth analysis of four gravitationally lensed red galaxies at z = 1.6-3.2. The sources are magnified by factors of 2.7-30 by foreground clusters, enabling spectral and morphological measurements that are otherwise challenging. Our sample extends below the characteristic mass of the stellar mass function and is thus more representative of the quiescent galaxy population at z > 1 than previous spectroscopic studies. We analyze deep VLT/X-SHOOTER spectra and multiband Hubble Space Telescope photometry that cover the rest-frame UV-to-optical regime. The entire sample resembles stellar disks as inferred from lensing-reconstructed images. Through stellar population synthesis analysis, we infer that the targets are young (median age = 0.1-1.2 Gyr) and formed 80% of their stellar masses within 0.07-0.47 Gyr. Mg ii lambda lambda 2796, 2803 absorption is detected across the sample. Blueshifted absorption and/or redshifted emission of Mg ii are found in the two youngest sources, indicative of a galactic-scale outflow of warm (T similar to 10(4) K) gas. The [O iii] lambda 5007 luminosity is higher for the two young sources (median age less than 0.4 Gyr) than the two older ones, perhaps suggesting a decline in nuclear activity as quenching proceeds. Despite high-velocity (v approximate to 1500 km s(-1)) galactic-scale outflows seen in the most recently quenched galaxies, warm gas is still present to some extent long after quenching. Altogether, our results indicate that star formation quenching at high redshift must have been a rapid process (