There are several potential sources from which the word "oorah" may have originated.
The term may have been derived from the Ottoman Turkish phrase "vur ha" translated as "strike" or the Mongolian word "urakh" meaning "rip off". It was used as a battle cry of the Ottoman Empire army and adapted as a Russian battle cry "ura".
According to Jean Paul Roux the word "Hurrah" comes from Old Turkic, in use until medieval times. In his book, History of Turks he states: "For example, while attacking to their enemies, they (Turks) used to shout "Ur Ah!" which means "Come on, hit!" (in modern Turkish "Vur Hadi!") Then this exclamation turned into "Hurrah!" in [the] West... The difference represents diachronic change in the phonology and verbal usage in Turkish. The verb for "to hit" or "to strike" was urmak, which became vurmak in Modern Turkish. Moreover, a former subjunctive imperative verbal ending of e/a is not productive in Modern Turkish. Therefore, "ura", meaning "may it hit", which would have changed phonetically to "vura" in Modern Turkish, is expressed with "vursun".
The term may have come from warriors of Ancient Hun or of Mongolian Empire "hurray" meaning "to move attack" or "appeal for goodness", which was formed into "(h)urra" in Russian with same meaning, and from which the Mongolia "Uria" (callings or slogans) comes from. "Hurray and Uria" words are used today in Mongolia from the ancient soldiers.
Jack Weatherford asserts that it comes from the Mongolian "hurree", used by Mongol armies and spread throughout the world during the Mongol Empire of the 13th century, but he does not appear to present any supporting evidence. Weatherford says that in Mongolian "hurree" is a sacred praise much like amen or hallelujah.
The term may have come from Middle High German of 1580–1590 "hurren" meaning "to move fast", which was formed into "hurra" and from which the English "hurry" comes. It is still used in the Netherlands and Dutch-speaking Belgium during celebrations in the form of "hoera", as well as in Sweden, Norway and Denmark as "hurra".
The term may be a variation of 18th century sailors exclamation "huzzah", traditionally said during salutes.
In World War II injured US Marines were treated in northern Australia. The term 'OoRah' is said to be local slang for 'farewell' or 'until then', although it is likely to be a mishearing of the more common 'ooroo'.
Marines are known to exclaim "Oorah" with a exaggerated growl to sound like a vicious canine. This growl/bark is representative of the nickname "Devil-Dogs," as Marines are known. The bark is similar in sound to the short bark of their official mascot, the Bulldog.
"Urrà" is traditionally the war cry of the Italian Army Bersaglieri Corps, since their return from the Crimean War. It is speculated that it comes from the Cossacks whose battle cry was Gu-Rai! which meant "Towards the bliss of heaven!"