We report optical spectroscopic observations of X-shaped radio sources with the Hobby-Eberly Telescope and Multiple-Mirror Telescope, focused on the sample of candidates from the FIRST survey presented in a previous paper. A total of 27 redshifts were successfully obtained, 21 of which are new, including a newly identified candidate source of this type which is presented here. With these observations, the sample of candidates from the previous paper is over 50% spectroscopically identified. Two new broad emission-lined X-shaped radio sources are revealed, while no emission lines were detected in about one-third of the observed sources; a detailed study of the line properties is deferred to a future paper. Finally, to explore their relation to the Fanaroff-Riley division, the radio luminosities and host galaxy absolute magnitudes of a spectroscopically identified sample of 50 X-shaped radio galaxies are calculated to determine their placement in the Owen-Ledlow plane.