The Orion Nebula Cluster (ONC) is the nearest dense star-forming region at ∼400 pc away, making it an ideal target to study the impact of high stellar density and proximity to massive stars (the Trapezium) on protoplanetary disk evolution. The OMC1 molecular cloud is a region of high extinction situated behind the Trapezium in which actively forming stars are shielded from the Trapezium's strong radiation. In this work, we survey disks at high resolution with ALMA at three wavelengths with resolutions of 0.095 (3 mm; Band 3), 0.048 (1.3 mm; Band 6), and 0.030 (0.85 mm; Band 7) centered on radio Source I. We detect 127 sources, including 15 new sources that have not previously been detected at any wavelength. 72 sources are spatially resolved at 3 mm, with sizes from ∼8 -100 AU. We classify 76 infrared-detected sources as foreground ONC disks and the remainder as embedded OMC1 disks. The two samples have similar disk sizes, but the OMC1 sources have a dense and centrally concentrated spatial distribution, indicating they may constitute a spatially distinct subcluster. We find smaller disk sizes and a lack of large (> 75 AU) disks in both our samples compared to other nearby star-forming regions, indicating that environmental disk truncation processes are significant. While photoevaporation from nearby massive Trapezium stars may account for the smaller disks in the ONC, the embedded sources in OMC1 are hidden from this radiation and thus must truncated by some other mechanism, possibly dynamical truncation or accretion-driven contraction.