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This would simply mean oaths from blood. They really mean it!
Crane uses the word crimson in regards to battle. These would be battle oaths, possibly angry and definitely impassioned. In the text, he emits “an outburst of crimson oaths” (Page 166) in response to the shame he feels at his initial shortcomings as a soldier.
The Red Badge of Courage
I think Jill actually has it right. It has more to do with anger and in line with everything else that is red in the rage of battle,
"Anger, although more non-physical than gunfire also seems naturally connected with the color red. At the end of the novel, Henry is ashamed of his initial shortcomings as a soldier and emits “an outburst of crimson oaths”"