Images of an 8 square arcmin region around the Orion KL source have been made in the J=7-6 (806 GHz) and J=4-3 (461 GHz) lines of CO with angular resolutions of 13" and 18". These data were taken employing on-the-fly mapping and position switching techniques. Our J=7-6 data set is the largest image of Orion with the highest sensitivity and resolution obtained so far in this line. Most of the extended emission arises from a photon dominated region (PDR), but 8% is associated with the Orion ridge. For the prominent Orion KL outflow, we produced ratios of the integrated intensities of our J=7-6 and 4-3 data to the J=2-1 line of CO. Large velocity gradient (LVG) models fit the outflow ratios better than PDR models. The LVG models give H2 densities of ∼105 cm–3. The CO outflow is probably heated by shocks. In the Orion S outflow, the CO line intensities are lower than for Orion KL. The 4-3/2-1 line ratio is 1.3 for the blueshifted wing and 0.8 for the redshifted wing. The line ratios in the Orion S outflow and jet features are consistent with both PDR and LVG models. Emission in the jet feature extending 2' to the SW of Orion S was detected in the J=4-3 but not the J=7-6 line; the average 4-3/2-1 line ratio is ∼1. Comparisons of the intensities of the J=7-6 and J=4-3 lines from the Orion Bar with PDR models show that the ratios exceed predictions by a factor of 2. Either clumping or additional heating by mechanisms, such as shocks, may be the cause of this discrepancy.