We aim to study the relative positions of quasar emission centers at different wavelengths in order to help link the various realizations of the International Celestial Reference System (ICRS), and to unveil systematic uncertainties and individual source behavior at different wavelengths. We based our study on four catalogs representing the ICRS, the ICRF3 positions in the three VLBI bands X, K, and Ka, and the Gaia EDR3 catalog in optical wavelengths. We complemented radio source positions with jet kinematics results from the MOJAVE team, allowing us to obtain jet directions on the sky. A six-parameter deformation model was used to remove systematic uncertainties present in the different catalogs. For a set of 194 objects common to the four catalogs and to the objects whose jet kinematics was studied by the MOJAVE team, we computed the orientation between positions at the different wavelengths and with respect to the directions of the jets. We find that the majority of these objects have their radio-to-optical vector along the jet, with the optical centroid downstream from the radio centroids, and that the K and Ka centroids are preferably upstream in the jet with respect to the X centroid, which is consistent with the paradigm of a simple core-jet model. For a population of multiwavelength positions aligned along the jet, astrometric information can therefore be used to measure the direction of the jet independently of imaging. In addition, we find several sources for which the optical centroid coincides with stationary radio features with a relatively high fraction of polarization, indicating optical emission dominated by a synchrotron process in the jet.