  We present SPHERE/IRDIS H-band data for a sample of 23 stars in the Orion
Star forming region observed within the DESTINYS (Disk Evolution Study Through
Imaging of Nearby Young Stars) program. We use polarization differential
imaging in order to detect scattered light from circumstellar dust. From the
scattered light observations we characterize the disk orientation, radius and
contrast. We analyse the disks in context of the stellar parameters and the
environment of the Orion star-forming region. We use ancillary X-shooter
spectroscopic observations to characterize the central stars in the systems. We
furthermore use a combination of new and archival ALMA mm-continuum
observations to characterize the dust masses present in the circumstellar
disks. Within our sample we detect extended circumstellar disks in 10 of 23
systems. Of these, three are exceptionally extended (V351 Ori, V599 Ori and
V1012 Ori) and show scattered light asymmetries which may indicate
perturbations by embedded planets or (in the case of V599 Ori) by an outer
stellar companion. Our high resolution imaging observations are also sensitive
to close (sub)stellar companions and we detect 9 such objects in our sample of
which 5 were previously unknown. We find in particular a possible sub-stellar
companion (either a very low mass star or a high mass brown dwarf) 137 au from
the star RY Ori. We find a strong anti-correlation between disk detection and
multiplicity, with only 2 of our 10 disk detections located in stellar multiple
systems. We also find a correlation between scattered light contrast and the
millimetre flux suggesting that disks that have a high dust content are
typically bright in near-infrared scattered light. Conversely we do not find
significant correlations between scattered light contrast of the disks and the
stellar mass or age.
