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 10:1NADAB AND ABIHU BURNT. (Lev. 10:1-20)
the sons of Aaron, &c.--If this incident occurred at the solemn period of the consecrating and dedicating the altar, these young men assumed an office which had been committed to Moses; or if it were some time after, it was an encroachment on duties which devolved on their father alone as the high priest. But the offense was of a far more aggravated nature than such a mere informality would imply. It consisted not only in their venturing unauthorized to perform the incense service--the highest and most solemn of the priestly offices--not only in their engaging together in a work which was the duty only of one, but in their presuming to intrude into the holy of holies, to which access was denied to all but the high priest alone. In this respect, "they offered strange fire before the Lord"; they were guilty of a presumptuous and unwarranted intrusion into a sacred office which did not belong to them. But their offense was more aggravated still; for instead of taking the fire which was put into their censers from the brazen altar, they seem to have been content with common fire and thus perpetrated an act which, considering the descent of the miraculous fire they had so recently witnessed and the solemn obligation under which they were laid to make use of that which was specially appropriated to the service of the altars, they betrayed a carelessness, an irreverence, a want of faith, most surprising and lamentable. A precedent of such evil tendency was dangerous, and it was imperatively necessary, therefore, as well for the priests themselves as for the sacred things, that a marked expression of the divine displeasure should be given for doing that which "God commanded them not."
lev 10:2there went out fire from the Lord, and devoured them--rather, "killed them"; for it appears (Lev 10:5) that neither their bodies nor their robes were consumed. The expression, "from the Lord," indicates that this fire issued from the most holy place. In the destruction of these two young priests by the infliction of an awful judgment, the wisdom of God observed the same course, in repressing the first instance of contempt for sacred things, as he did at the commencement of the Christian dispensation (Act 5:1-11).
lev 10:3Moses said . . . This is it that the Lord spoke . . . I will be sanctified in them that come nigh me--"They that come nigh me," points, in this passage, directly to the priests; and they had received repeated and solemn warnings as to the cautious and reverent manner of their approach into the divine presence (Exo 19:22; Exo 29:44; Lev 8:35).
Aaron held his peace--The loss of two sons in so sudden and awful a manner was a calamity overwhelming to parental feelings. But the pious priest indulged in no vehement ebullition of complaint and gave vent to no murmur of discontent, but submitted in silent resignation to what he saw was "the righteous judgment of God" [Rom 2:5].
lev 10:4Moses called Mishael and Elzaphan--The removal of the two corpses for burial without the camp would spread the painful intelligence throughout all the congregation; and the remembrance of so appalling a judgment could not fail to strike a salutary fear into the hearts both of priests and people. The interment of the priestly vestments along with Nadab and Abihu, was a sign of their being polluted by the sin of their irreligious wearers.
lev 10:6Uncover not your heads--They who were ordered to carry out the two bodies, being engaged in their sacred duties, were forbidden to remove their turbans, in conformity with the usual customs of mourning; and the prohibition "neither rend your garments," was, in all probability, confined also to their official costume. For at other times the priests wore the ordinary dress of their countrymen and, in common with their families, might indulge their private feelings by the usual signs or expressions of grief.
lev 10:8Do not drink wine nor strong drink--This prohibition, and the accompanying admonitions, following immediately the occurrence of so fatal a catastrophe [Lev 10:1-2], has given rise to an opinion entertained by many, that the two disobedient priests were under the influence of intoxication when they committed the offense which was expiated only by their lives. But such an idea, though the presumption is in its favor, is nothing more than conjecture.
lev 10:12Moses spake unto Aaron, &c.--This was a timely and considerate rehearsal of the laws that regulated the conduct of the priests. Amid the distractions of their family bereavement, Aaron and his surviving sons might have forgotten or overlooked some of their duties.
lev 10:16Moses diligently sought the goat of the sin offering, and, behold, it was burnt--In a sacrifice presented, as that had been, on behalf of the people, it was the duty of the priests, as typically representing them and bearing their sins, to have eaten the flesh after the blood had been sprinkled upon the altar. Instead of using it, however, for a sacred feast, they had burnt it without the camp; and Moses, who discovered this departure from the prescribed ritual, probably from a dread of some further chastisements, challenged, not Aaron, whose heart was too much lacerated to bear a new cause of distress but his two surviving sons in the priesthood for the great irregularity. Their father, however, who heard the charge and by whose directions the error had been committed, hastened to give the explanation. The import of his apology is, that all the duty pertaining to the presentation of the offering had been duly and sacredly performed, except the festive part of the observance, which privately devolved upon the priest and his family. And that this had been omitted, either because his heart was too dejected to join in the celebration of a cheerful feast, or that he supposed, from the appalling judgments that had been inflicted, that all the services of that occasion were so vitiated that he did not complete them. Aaron was decidedly in the wrong. By the express command of God, the sin offering was to be eaten in the holy place; and no fanciful view of expediency or propriety ought to have led him to dispense at discretion with a positive statute. The law of God was clear and, where that is the case, it is sin to deviate a hair's breadth from the path of duty. But Moses sympathized with his deeply afflicted brother and, having pointed out the error, said no more.