What is the meaning of the strange fire in Leviticus 10:1? Nadab and Abihu were killed for this "small" thing in God's eyes.  Wow!  I have a hard time understanding this.  Any thoughts?
In Jewish times, the source of the fire in the sanctuary was from God. Initially, when they first laid the sacrifice as an offering at the alter, fire was literally sent from God and consumed it (Leviticus 9:24). Since then it was to be kept continually burning. (Leviticus 6:12-13).

Thus Nadab and Abihu displayed wanton presumptuousness by lighting fire themselves in the censer (instead using fire from the alter) and offering it to the Lord. As if such a disingenuous act would go unnoticed and accepted by God Himself. They rejected God's mercy for the last time, and were stricken down.

Finally, the smoke of the censer represent the cleansing of the prayers of the believers before it reaches God (Revelation 8:4). For them to use human means at a time when divine fire was available and required was incredibly profane.