Ten protostellar outflows in the Orion molecular clouds were mapped in the $^{12}$CO/$^{13}$CO ${J=6rightarrow5}$ and $^{12}$CO ${J=7rightarrow6}$ lines. The maps of these mid-$J$ CO lines have an angular resolution of about 10$$ and a typical field size of about 100$$. Physical parameters of the molecular outflows were derived, including mass transfer rates, kinetic luminosities, and outflow forces. The outflow sample was expanded by re-analyzing archival data of nearby low-luminosity protostars, to cover a wide range of bolometric luminosities. Outflow parameters derived from other transitions of CO were compared. The mid-$J$ ($J_{rm up} approx 6$) and low-$J$ ($J_{rm up} leq 3$) CO line wings trace essentially the same outflow component. By contrast, the high-$J$ (up to $J_{rm up} approx 50$) line-emission luminosity of CO shows little correlation with the kinetic luminosity from the ${J=6rightarrow5}$ line, which suggests that they trace distinct components. The low/mid-$J$ CO line wings trace long-term outflow behaviors while the high-$J$ CO lines are sensitive to short-term activities. The correlations between the outflow parameters and protostellar properties are presented, which shows that the strengths of molecular outflows increase with bolometric luminosity and envelope mass.
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