I read a lot of books from TL and, it seems, I have enough game experience, but in this question I really need help. So, how Orsimer greet and treat each other? Do they have specific etiquette of speaking (besides prefixes gra- and gro-) ? I may suppose, that City Orcs, especially if they have lived for tens years near Imperials, have adopted Imperial style. But, is there any difference?
Please, teach me, honour members of Elder Scroll Lore forum!

http://www.imperial-library.info/content/code-malacath is your answer. Also, all males are considered rivals to the chief.

I was about to say "that it's only males seems odd for a culture that's been noted as being particularly gender-egalitarian for a continent that is itself generally pretty good in that regard", but then again that was the more cosmopolitan, assimilationist Orsinium-based culture, so I suppose the culture of the strongholds could be different.

(I'd also like to note that the Code of Malacath bears, in several places, a resemblance to the organisation of Ashlander culture. Coincidence? Borrowing? Convergent evolution involving two different groups living in small bands separated from settled society?)

Having your civilization destroyed three or four times tends to set six relations back a bit.

More likely, it's more to do with the fact that both have quite a bit of Mongolian culture thrown into them.

Thank you for useful link, but this subject still is not clear to me. At the very first view, Orsimer are persented in TES both as blood-thirsty warriors and as alcoholic (not rarely) slow-minded bumpkins (a city version). If we take the first case, are there any specific words, expressions or rituals in their conversation. Do they have codex of honour like Mongolian, mentioned by Saint_Jiub? Are there any in-game hints?