A state-selected beam of hydroxyl radicals is generated using a pulsed discharge source and hexapole field. The OH radicals are characterized by resonance-enhanced multiphoton ionization (REMPI) spectroscopy via the nested D 2Sigma- and 3 2Sigma- Rydberg states. Simplified spectra are observed from the selected |MJ|=3/2 component of the upper Lambda-doublet level of the lowest rotational state (J=32) in ground (v"=0) and excited (v"=1-3) vibrational levels of the OH X 2Pi3/2 state. Two-photon transitions are observed to the D 2Sigma-(v'=0-3) and 3 2Sigma-(v'=0,1) vibronic levels, extending previous studies to higher vibrational levels of the Rydberg states. Spectroscopic constants are derived for the Rydberg states and compared with prior experimental studies. Complementary first-principle theoretical studies of the properties of the D 2Sigma- and 3 2Sigma- Rydberg states [see M. P. J. van der Loo and G. C. Groenenboom, J. Chem. Phys. 123, 074310 (2005), following paper] are used to interpret the experimental findings and examine the utility of the (2+1) REMPI scheme for sensitive detection of OH radicals.