What did they do with their bodies outside the camp?
Ramban: Moshe commanded them to take them outside the camp and to then remove their Bigdei Kehunah and dress them in shrouds.
Targum Yonasan: They buried them there.
Seeing as Misha'el and Eltzafan were Levi'im and were not permitted to enter the Heichal, how did they remove Nadav and Avihu?
Targum Yonasan: They pulled them out using metal hooks which they threw inside and which hooked on to their shirts (R. Akiva in Toras Kohanim - they pulled them out via a spear.)
R. Eliezer, in Toras Kohanim: An angel struck them inside and expelled them (outside the Mishkan).
The Sifra discusses making a plating for the walls of the Heichal, and not Tum'ah. (PF)
Why does the Torah find it necessary to inform us that they took them out in their Kutanos?
Rashi: To teach us that their clothes were not burned, only their Neshamos. 1
Ramban: Refer to 10:5:1:1.
Seforno: This teaches us that they did not bother to remove the Bigdei Kehunah before leaving the camp, since they had become Tamei anyway.
Via two strips of fire that entered their nostrils (Rashi).
Sifra says that their bodies were burned, but not their clothes. Why does it say in Sukah (25b) that Misha'el and Eltzafan were Tamei Mes due to Nadav and Avihu? A burned body is not Metamei (Nidah 27b)!
Moshav Zekenim: The Sheled (Hadar Zekenim - spine and ribs 1 ) was intact. In such a case, it is Metamei (Nidah 27b).
Moshav Zekenim citing R. Shemayah: They were quivering. He wavered about [answering based on] the Gemara in Nidah. (Refer to 10:5:151:1.)
Hadar Zekenim: When they fell, the Sheled collapsed. Why were they Metamei? We must say that they fell gently, and the Sheled was intact.