From Very Long Baseline Array (VLBA) observations we previously identified a population of 123 young stellar systems with nonthermal radio emission toward the core of the Orion Nebula Cluster (ONC). We find optical sources in the Gaia DR2 catalog for 34 of them within 0.2 of the radio positions. Most of the radio sources are likely companions of Gaia detections. However, there are 11 stars whose VLBA positions differ from Gaia by <1.6mas, and some of these radio sources probably are the direct counterparts of the optical stars. We are able to obtain radio proper motions for 23 stars. Combining the stellar proper motions derived from the VLBA and Gaia DR2 data we find the global motion and velocity dispersion of the ONC to be ({mu}{alpha}*,{mu}{delta})=(1.20{+/-}0.09,0.18{+/-}0.09)mas/yr and ({sigma}_{mu}_{alpha}__,{sigma}_{mu}_{delta}__)=(0.84{+/-}0.09,1.30{+/ -}0.09)mas/yr. Finally, we looked for ordered motions by estimating the means of scalar and vectorial products, which results in \overline{nu}.r=-0.61{+/-}1.00km/s and {nu}xr=0.57{+/-}0.95km/s. These do not show indications that the young stellar cluster is in expansion, contraction, or rotation.