Why did they die through fire that went out from before Hashem?
Targum Yonasan: It is a sign of Hashem's Midas ha'Din that emerged in anger from before Hashem. 1
Tosfos ha'Shalem 2 (2): This was Midah k'Neged Midah .They saw fire descend from Shamayim, and wanted to offer a strange fire. Hashem said, let us see whose fire will win - Mine or yours?!
The verse says that they died "Lifnei Hashem". Where was this?
Rosh, Moshav Zekenim and Da'as Zekenim, citing R. Eliezer in Toras Kohanim: An angel struck them inside and expelled them (outside the Mishkan) before they died, to where Leviyim may go (Misha'el and Eltzafan - verse 4).
Rosh, Moshav Zekenim and Da'as Zekenim, citing R. Akiva in Toras Kohanim: They died inside (the Mishkan), Misha'el and Eltzafan put iron hooks in their mouths in order to take them out. 1
Moshav Zekenim: Since it was possible to remove them through Chanis (a spear? - PF), there was no Heter to enter the Mishkan.
In Toras Kohanim, R. Akiva says that that they died inside. If so, they were Metamei the Mishkan, which is called Ohel. We do not find that they ceased from the Avodah - "umi'Pesach Ohel Mo'ed Lo Setz'u" (verse 7)!
Tosfos ha'Shalem (2): They were Chayav Misah Lifnei Hashem, but they died only outside.
Moshav Zekenim (4, citing the Rosh): Since it says "Al Pi Hashem Tachanu v'Al Pi Hashem Yis'u", [the Mishkan] is considered (attached), and it cannot become Tamei. 1
I do not know why Rosh, Da'as Zekenim and Hadar Zekenim left this difficult. Even if the Mishkan received Tum'as Ohel, Kohanim may enter after the Mes is removed; the Ohel is not Metamei them (Gur Aryeh Bamidbar 19:14.) Korbanos Tzibur override Tum'ah. This includes the Nesi'im's Korbanos, for they overrode Shabbos! (PF)
In Toras Kohanim, R. Akiva says that that they died inside. If so, they were Metamei the Kelim. Parah Adumah was not burned until the next day. How did they serve after this?
Refer to 10:2:152:1.
Moshav Zekenim (4): They were Makdish other Kelim temporarily and served with them.
Sanhedrin 52a expounds that the fire consumed "Osam", and not their garments. We already know this, for they were removed in their garments (verse 5)!