We have selected a sample of 80 candidates for obscured radio-loud active galactic nuclei and presented their basic optical/near-infrared (NIR) properties in Paper 1. In this paper, we present both high-resolution radio continuum images for all of these sources and HI 21cm absorption spectroscopy for a few selected sources in this sample. A-configuration 4.9 and 8.5 GHz VLA continuum observations find that 52 sources are compact or have substantial compact components with size <0.5 and flux density >0.1 Jy at 4.9 GHz. The most compact 36 sources were then observed with the VLBA at 1.4 GHz. One definite and 10 candidate Compact Symmetric Objects (CSOs) are newly identified, a detection rate of CSOs ~3 times higher than the detection rate previously found in purely flux-limited samples. Based on possessing compact components with high flux densities, 60 of these sources are good candidates for absorption-line searches. Twenty seven sources were observed for HI 21cm absorption at their photometric or spectroscopic redshifts with only 6 detections made (one detection is tentative). However, five of these were from a small subset of six CSOs with pure galaxy optical/NIR spectra and for which accurate spectroscopic redshifts place the redshifted 21cm line in a RFI-free spectral window. It is likely that the presence of ubiquitous RFI and the absence of accurate spectroscopic redshifts preclude HI detections in similar sources (only one detection out of the remaining 22 sources observed, 14 of which have only photometric redshifts). Future searches for highly-redshifted HI and molecular absorption can easily find more distant CSOs among bright, blank field radio sources but will be severely hampered by an inability to determine accurate spectroscopic redshifts for them due to their lack of rest-frame UV continuum.
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