Notes (NET Translation)
10:1 Then Aaron’s sons, Nadab and Abihu, each took his fire pan and put fire in it, set incense on it, and presented strange fire before the Lord, which he had not commanded them to do.
It is the eighth day of the inauguration and the sacrifices have been offered  but not eaten by the priests . Nadab and Abihu were Aaron’s oldest sons. They put embers/coals (esh) in their fire pans. “Incense was produced by mixing aromatic spices together, which were then vaporized by putting them in a censer containing glowing lumps of charcoal” . The phrase “strange fire” (esh zarah) refers to the coals. The exact nature of the transgression is veiled but it involved an illicit cultic act of some kind. Perhaps they took the coals from a profane source and not the outer altar. Lev. 16:1-2 recalls this event and may imply that Nadab and Abihu penetrated too far into the sanctuary, namely beyond the veil-canopy into the Holy of Holies. But, as we shall see, it does not appear that Nadab and Abihu made it that far. If Ex. 30:9 refers to the same kind of transgression with the words ketoret zarah then it would seem Nadab and Abihu erred by offering something other than the daily incense offering on the golden incense altar. But the focus seems to be on the coals/fire and not the incense. The key point is that they did something that they had not been commanded to do.
2 So fire went out from the presence of the Lord and consumed them so that they died before the Lord.
In 9:24 fire came out of the Tent of Meeting to consume the sacrifice offered at the dedication of the Tabernacle while in this verse it came out to kill Nadab and Abihu. Strange fire is punished by divine fire. Verse 5 states that their bodies were carried away and therefore they were not incinerated.
3 Moses then said to Aaron, “This is what the Lord spoke: ‘Among the ones close to me I will show myself holy, and in the presence of all the people I will be honored.'” So Aaron kept silent.
The “ones close to me” are the priests . Moses tells Aaron that God has revealed his holiness through the death of Nadab and Abihu. The reason Aaron is silent is not clear. Is he silent because of his grief? Is he silent because of God’s holiness? Do Moses’ words provide solace? Whatever the reason, he does not lash out at God.
4 Moses then called to Mishael and Elzaphan, the sons of Uzziel, Aaron’s uncle, and said to them, “Come near, carry your brothers away from the front of the sanctuary to a place outside the camp.”
Officiating priests could not handle the dead . Nothing else is known of Mishael, but Elzaphan was the head of the Kohathites . That the bodies were in “the front of the sanctuary” and that the blood of the sin offering was not brought into the sanctuary  implies that Nadab and Abihu were killed before they entered the Tent of Meeting. They were struck down in the courtyard.
5 So they came near and carried them away in their tunics to a place outside the camp just as Moses had spoken.
The tunics are those of Nadab and Abihu .
6 Then Moses said to Aaron and to Eleazar and Ithamar his other two sons, “Do not dishevel the hair of your heads and do not tear your garments, so that you do not die and so that wrath does not come on the whole congregation. Your brothers, all the house of Israel, are to mourn the burning which the Lord has caused, 7 but you must not go out from the entrance of the Meeting Tent lest you die, for the Lord’s anointing oil is on you.” So they acted according to the word of Moses.
Aaron, Eleazar, and Ithamar are not to mourn Nadab and Abihu by disheveling their hair or tearing their garments. The house of Israel will mourn on behalf of Aaron and his remaining sons. Normally just the high priest would abstain from mourning , but since Eleazar and Ithamar has been specially anointed  they too must abstain from mourning. Eleazar and Ithamar were anointed in a way that future generations of priests, except for the future high priests, were not.
8 Then the Lord spoke to Aaron, 9 “Do not drink wine or strong drink, you and your sons with you, when you enter into the Meeting Tent, so that you do not die, which is a perpetual statute throughout your generations, 10 as well as to distinguish between the holy and the common, and between the unclean and the clean, 11 and to teach the Israelites all the statutes that the Lord has spoken to them through Moses.”
This is the only place in Leviticus where God addresses Aaron alone (not through Moses). Aaron is still the high priest despite the transgression of his sons. Priests must avoid all intoxicating drinks so that they can properly fulfill their duties. One might speculate that this prohibition is mentioned here because it played a role in the death of Nadab and Abihu .
12 Then Moses spoke to Aaron and to Eleazar and Ithamar, his remaining sons, “Take the grain offering which remains from the gifts of the Lord and eat it unleavened beside the altar, for it is most holy.
The eighth day of the inauguration continues. The food on the altar had not been consumed after the death of Nadab and Abihu.
13 You must eat it in a holy place because it is your allotted portion and the allotted portion of your sons from the gifts of the Lord, for this is what I have been commanded.
14 Also, the breast of the wave offering and the thigh of the contribution offering you must eat in a ceremonially clean place, you and your sons and daughters with you, for they have been given as your allotted portion and the allotted portion of your sons from the peace offering sacrifices of the Israelites.
15 The thigh of the contribution offering and the breast of the wave offering they must bring in addition to the gifts of the fat parts to wave them as a wave offering before the Lord, and it will belong to you and your sons with you for a perpetual statute just as the Lord has commanded.”
16 Later Moses sought diligently for the sin offering male goat, but it had actually been burnt. So he became angry at Eleazar and Ithamar, Aaron’s remaining sons, saying, 17 “Why did you not eat the sin offering in the sanctuary? For it is most holy and he gave it to you to bear the iniquity of the congregation, to make atonement on their behalf before the Lord. 18 See here! Its blood was not brought into the holy place within! You should certainly have eaten it in the sanctuary just as I commanded!”
A sin offering on behalf of the people should have been consumed by the priests . If the blood had been brought into the holy place then the animal should have been burnt outside the sanctuary . Moses holds the priests guilty for not eating the meat.
19 But Aaron spoke to Moses, “See here! Just today they presented their sin offering and their burnt offering before the Lord and such things as these have happened to me! If I had eaten a sin offering today would the Lord have been pleased?”
Aaron acted deliberately. He is saying, “In light of today’s tragic events, my eating of the sin offering would not have been pleasing to God.” Deut. 26:14 implies that mourners were not to partake of devoted foods, yet Aaron and his sons were not to mourn so it is not clear that said verse should apply to this passage. Milgrom hypothesizes that because Nadab and Abihu were killed before the meat was eaten, Aaron may have thought their corpses contaiminated the sacrifice to such an extent that the meat should not be ingested .
20 When Moses heard this explanation, he was satisfied.
This incident stands in marked contrast to the tragedy at the beginning of this chapter. It is recorded to illustrate that the priests have some freedom in applying the regulations to daily situations as long as their interpretation does not tarnish God’s holiness. Furthermore, it illustrates how the priests are to resolve disputes about the law. Two prominent priests debated the issue, with the one convincing the other as to the proper response on the basis of a sound argument. The remarkable feature of this account is that the lesser figure, Aaron, persuaded the greater figure, Moses. Thus a dispute about the law is to be resolved by sound judgment presented in open discussion rather than by one person’s vaunting of authority. This incident also reveals that Aaron, though he could not formally mourn the death of his sons, felt the pain of their loss deeply and expressed his mourning in a quiet, but definitive manner. The concession made to Aaron shows that Yahweh is not unsympathetic to human sorrow caused by his judgment against wickedness. 
The tension between Aaron’s deviation from the regulations with God’s approval and the deviation of his sons, resulting in God’s immediate and final judgment, sets forth the teaching that there are proper and improper ways to deviate from a given regulation. The regulations are standards set to honor God and to promote his holiness. Any alteration of a standard that dishonors God will be confronted by God’s consuming holiness. The priests then are to guard themselves from blatantly violating the sacred. However, any variation based on sound reason backed by the motivation to give glory to God is tolerable and acceptable. 
 Lev. 9:8-21
 Lev. 10:12-20
 Wenham 1979, loc. 2046-2047
 Ezek. 42:13; 43:19
 Lev. 21:1-4, 10-12
 Num. 3:30; cf. 1 Chr. 15:8; 2 Chr. 29:13
 Lev. 10:18
 Milgrom 1991, p. 606
 Lev. 21:12
 Ex. 40:15; Num. 3:3
 Pesiq. Rab Kah. 26:9; Midr. Lev. Rab. 20:9
 Lev. 6:25-26, 29
 Lev. 4:1-21
 Milgrom 1991, p. 639
 Hartley 1998, p. 137
 Hartley 1998, p. 138
Hartley, John E. Leviticus. Dallas, Tex.: Word Books, 1992.
Levine, Baruch A. Leviticus. Philadelphia: Jewish Publication Society, 1989.
Milgrom, Jacob. Leviticus 1-16. New York: Doubleday, 1991.
Rooker, Mark, and Dennis R. Cole. Leviticus. Kindle Edition. Holman Reference, 2000.
Wenham, Gordon J. The Book of Leviticus. Kindle Edition. Wm. B. Eerdmans Publishing Company, 1979.