Observations made with the U.S. Naval Observatory 20 cm transit telescope are presented for 104 FK5 and 13 radio stars that are directly tied into the J2000 extragalactic reference system. A comparison of the star positions presented in this paper with the FK5 catalog finds possible warps in the FK5 reference system with amplitudes approximately 0.1 arcsec and rotations for linking the optical and radio reference systems with values omega(x) = -20 +/- 17 (s.e.), omega(y) = 28 +/- 16 (s.e.), and omega(z) = 11 +/- 13 (s.e.) mas. When the data of this paper are combined with other studies, these rotations become omega(x) = 11 +/- 13 (s.e.), omega(y) = 40 +/- 13 (s.e.), and omega(z) = 17 +/- 9 (s.e.) mas, indicating the omega(y) rotation might be real. Among the radio stars, there are four stars (KQ Pup, 54 Cam, SZ Psc, and HD 244085) with significant optical-radio offsets that exceed 0.15 arcsec in magnitude. Moreover, many other radio stars probably have appreciable offsets as determined from a statistical investigation. Optical-radio offsets which are typically accurate to sigma approximately +/-42 (s.e.) mas are also presented for 48 extragalactic objects observed with the transit telescope. Among these objects, 21% have significant offsets. Radio galaxies are much more likely to have large offsets than QSOs and BL Lac objects, making many of them poor candidates for radio reference objects.