A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
lev 7:1THE LAW OF THE TRESPASS OFFERING. (Lev. 7:1-27)
Likewise this is the law of the trespass offering--This chapter is a continuation of the laws that were to regulate the duty of the priests respecting the trespass offerings. The same regulations obtained in this case as in the burnt offerings--part was to be consumed on the altar, while the other part was a perquisite of the priests--some fell exclusively to the officiating minister, and was the fee for his services; others were the common share of all the priestly order, who lived upon them as their provision, and whose meetings at a common table would tend to promote brotherly harmony and friendship.
lev 7:8the priest shall have to himself the skin of the burnt offering which he hath offered--All the flesh and the fat of the burnt offerings being consumed, nothing remained to the priest but the skin. It has been thought that this was a patriarchal usage, incorporated with the Mosaic law, and that the right of the sacrificer to the skin of the victim was transmitted from the example of Adam (see on Gen 3:21).
lev 7:11this is the law of the sacrifice of peace offerings--Besides the usual accompaniments of other sacrifices, leavened bread was offered with the peace offerings, as a thanksgiving, such bread being common at feasts.
lev 7:15the flesh of the sacrifice of his peace offerings . . . shall be eaten the same day that it is offered--The flesh of the sacrifices was eaten on the day of the offering or on the day following. But if any part of it remained till the third day, it was, instead of being made use of, to be burned with fire. In the East, butcher-meat is generally eaten the day it is killed, and it is rarely kept a second day, so that as a prohibition was issued against any of the flesh in the peace offerings being used on the third day, it has been thought, not without reason, that this injunction must have been given to prevent a superstitious notion arising that there was some virtue or holiness belonging to it.
lev 7:18if any of the flesh of the sacrifice . . . be eaten at all on the third day, it shall not be accepted, neither . . . imputed--The sacrifice will not be acceptable to God nor profitable to him that offers it.
lev 7:20cut off from his people--that is, excluded from the privileges of an Israelite--lie under a sentence of excommunication.
lev 7:21abominable unclean thing--Some copies of the Bible read, "any reptile."
lev 7:22Ye shall eat no manner of fat--(See on Lev 3:17).
lev 7:29THE PRIESTS' PORTION. (Lev 7:28-38)
He that offereth the sacrifice of his peace offerings unto the Lord--In order to show that the sacrifice was voluntary, the offerer was required to bring it with his own hands to the priest. The breast having been waved to and fro in a solemn manner as devoted to God, was given to the priests; it was assigned to the use of their order generally, but the right shoulder was the perquisite of the officiating priest.
lev 7:35This is the portion of the anointing of Aaron--These verses contain a general summing up of the laws which regulate the privileges and duties of the priests. The word "anointing" is often used as synonymous with "office" or "dignity." So that the "portion of the anointing of Aaron" probably means the provision made for the maintenance of the high priest and the numerous body of functionaries which composed the sacerdotal order.
in the day when he presented them to minister unto the Lord, &c.--that is, from the day they approached the Lord in the duties of their ministry.