How strong was Yugoslav identity within the country itself?
According to the population census of 1981 (the last one before breakup), only 5.4% people declared themselves Yugoslav. The census of 1971 that number was even lower 1.2%
Based on that data, and the various personal annegdotes one might easily find, I would conclude that people were primarily thinking of themselves as Serbs, Croats and their respective nations.
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Are you referring to the term "Yugoslav" as in demographics? It was used mostly by people in mixed marriages and others who identified very strongly with the country - about 5% of them at most, according to the census.