Wiktionary gives this:
Irish Osgar, from os (“deer”) + cara (“friend”) ; resuscitated by James Mcpherson in The Works of Ossian (1765). Napoleon, an admirer of the Ossianic poems, chose it for his godson Oscar Bernadotte, who became a king of Sweden.
It can also be explained by Old English ōs (“god”) and gār (“spear”) (see Oswald, Osborn, Oswid, Osric, Oslak).
While Wikipedia states that:
The name is derived from two elements in Irish: the first, os, means "deer"; the second element, cara, means "friend". The name is borne by a character in Irish mythology—Oscar, grandson of Fionn Mac Cumhail. The name was popularised in the 18th century by James Macpherson, creator of "Ossianic poetry". Today the name is associated with Scandinavia because Napoleon was an admirer of Macpherson's work and gave the name to his godson, Oscar Bernadotte, who later became Oscar I, King of Sweden.1
The given name Oscar is not to be confused with the Old English Ōsgār, which is of an entirely different origin (from two Old English elements meaning "god" and "spear").2
So the question is: What is the real origin of "Oscar", Irish or OE?