The sprinkling with oil and blood completes the ceremony of anointing, and suffices of itself for the sons of Aaron, in addition to their virtual participation in the anointing of their father (Leviticus 8:12). "In the mingling of the blood and oil for the anointing seems to be taught that not sacrifice for sin alone suffices; but that with this must be joined the unction of the Holy Spirit" (Gardiner).
The flesh of the peace offering is given to Aaron and his sons to eat, not in the capacity of priests (for the peace offerings were not eaten by the priests), but as the offerers of the sacrifice.