We analyze the spatial distribution of dusty young stellar objects (YSOs) identified in the Spitzer Survey of the Orion Molecular clouds, augmenting these data with Chandra X-ray observations to correct for incompleteness in dense clustered regions. We also devise a scheme to correct for spatially varying incompleteness when X-ray data are not available. The local surface densities of the YSOs range from 1 pc$^{-2}$ to over 10,000 pc$^{-2}$, with protostars tending to be in higher density regions. This range of densities is similar to other surveyed molecular clouds with clusters, but broader than clouds without clusters. By identifying clusters and groups as continuous regions with surface densities $ge10$ pc$^{-2}$, we find that 59% of the YSOs are in the largest cluster, the Orion Nebular Cluster (ONC), while 13% of the YSOs are found in a distributed population. A lower fraction of protostars in the distributed population is evidence that it is somewhat older than the groups and clusters. An examination of the structural properties of the clusters and groups show that the peak surface densities of the clusters increase approximately linearly with the number of members. Furthermore, all clusters with more than 70 members exhibit asymmetric and/or highly elongated structures. The ONC becomes azimuthally symmetric in the inner 0.1 pc, suggesting that the cluster is only $sim 2$ Myr in age. We find the star formation efficiency (SFE) of the Orion B cloud is unusually low, and that the SFEs of individual groups and clusters are an order of magnitude higher than those of the clouds. Finally, we discuss the relationship between the young low mass stars in the Orion clouds and the Orion OB 1 association, and we determine upper limits to the fraction of disks that may be affected by UV radiation from OB stars or by dynamical interactions in dense, clustered regions.
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