I started reading your post and thought, "Chaotic Neutral, for sure." Then, by the end, I was thinking, "Lawful Neutral."
Where I run into problems is when you said that they have a policy that the strongest warrior gets to take what he wants. This would seem to go against LN, which would have a rigid structure for deciding who gets what, who can challenge whom, etc. Having a "To the victor go the spoils" attitude seems rather chaotic to me. To me, a Lawful society can't survive as such if a stronger unstart could come along and topple the lawful government just by being stronger than the ruler. In a Lawful society, even Lawful Neutral, there would be laws and organizations built to adjudicate and avoid such confrontations. I imagine your orcs as living by a code of honor and tradition passed down for generations, but they would seem to follow it mostly because it's a good idea, not from any innate sense of lawfulness.
Therefore, I would say your orc society is, at its base, True Neutral. Rulers might be Lawful or Chaotic, but the society itself tends both ways enough to balance out one or the other.