Recently published high-quality OmegaCAM photometry of the 3x3deg around the Orion Nebula Cluster (ONC) in r, and i filters revealed three well-separated pre-main sequences in the color-magnitude diagram (CMD). The objects belonging to the individual sequences are concentrated toward the center of the ONC. The authors concluded that there are two competitive scenarios: a population of unresolved binaries and triples with an exotic mass ratio distribution, or three stellar populations with different ages (~=1Myr age differences). We use Gaia DR2 in combination with the photometric OmegaCAM catalog to test and confirm the presence of the putative three stellar populations. We also study multiple stellar systems in the ONC for the first time using Gaia DR2. We selected ONC members based on parallaxes and proper motions and take advantage from OmegaCAM photometry that performs better than Gaia DR2 photometry in crowded regions. We identify two clearly separated sequences with a third suggested by the data. We used Pisa stellar isochrones to estimate ages of the stellar populations with absolute magnitudes computed using Gaia parallaxes on a star by star basis. (1) We confirm that the second and third sequence members are more centrally concentrated toward the center of the ONC. In addition we find an indication that the parallax and proper motion distributions are different among the members of the stellar sequences. The age difference among stellar populations is estimated to be 1-2Myr. (2) We use Gaia proper motions and other measures to identify and remove as many unresolved multiple system candidates as possible. Nevertheless we are still able to recover two well-separated sequences with evidence for the third one, supporting the existence of the three stellar populations. (3) Due to having ONC members with negligible fore- or background contamination we were able to identify a substantial number of wide binary objects (separation between 1000 and 3000 au) and with relative proper motions of the binary components consistent with zero. This challenges previously inferred values that suggested no wide binary stars exist in the ONC. Our inferred wide-binary fraction is ~=5%. We confirm the three populations correspond to three separated episodes of star formation. Based on this result, we conclude that star formation is not happening in a single burst in this region. In addition we identify 5% of wide-binary stars in the ONC that were thought not to be present.