The type of yeast strain used for wine alcoholic fermentation dramatically affects its final volatile composition and, therefore, its sensory properties. In this study, the influence of four oenological Saccharomyces strains (three S. cerevisiae and one S. bayanus) on wine volatile composition was determined on the Fiano variety, a typical cultivar from the Campania region (Italy), fermented in oak barrique. Fiano wines were analyzed by means of gas chromatography/mass spectrometry (GC/MS) and gas chromatography/olfactometry (GC/O). The results showed that the four selected yeast strains had a significant impact on the majority of volatile compounds as shown by the concentration of volatile compounds and based on the Aroma Extract Dilution Analysis (AEDA) values for many of the odor volatile compounds. This resulted in a dramatic change of the odor impact of the wines, such as the “fruity” attribute, which was higher compared to the control, and caused some changes of other odor attributes, particularly “floral”, “phenolic” and “honey”. This research demonstrates the potential of using these selected yeast strains and this technological approach of oak fermentation for this typical white wine grape variety.