Or HaChaim on Leviticus 10:6/אור החיים על ויקרא י׳:ו׳

1 ראשיכם אל תפרעו; "do not let the hair of your head grow wild." The Torah warns that if the people at large were to do the same as the priests, i.e. trim their hair while in mourning for a close relative, G'd would become angry. There are differences in the manner ordinary Israelites mourn their dead and in the manner in which priests charged with serving the Lord do this. Whereas the priests are not allowed to let their hair grow wild, they are obligated to rend their garments when hearing of the death of a close relative. Perhaps, in this instance, the rules applied were those we apply when the president of the Supreme Court dies; at such a time all of Israel are commanded to rend their garments as a sign of mourning (Moed Katan 22). In view of the opinion that Nadav and Avihu were of greater stature than even Moses and Aaron, it was certainly appropriate for the whole nation to mourn their deaths.

2ואחיכם כל בית ישראל יבכו, "and your brethren the whole house of Israel will weep, etc." This is a מצוה, a desirable act; failure to do so will not arouse G'd's anger. The Torah is particular to write אשר שרף השם. This may best be understood in accordance with a statement in Shabbat 105 that anyone who weeps and mourns another person' death has his own sins forgiven and will not have cause to weep [for a tragedy in his immediate family. Ed.]. This thought is alluded to in the words אשר שרף, "He had burned." If the Israelites were to weep for the death of Nadav and Avihu now, there would be no future burning to be wept for. The words ולא תמותו ועל כל העדה יקצוף "so that you will not die and G'd will be angry at the whole congregation" mean, that when the righteous die G'd's anger is unleashed against the whole of Israel. The reason is that the righteous by their very existence had kept G'd's anger against Israel in check while they were alive. The death of priests is especially apt to result in G'd's anger becoming manifest as it was the task of the priest to assuage G'd's anger by means of the Temple service he performed while alive.