In the framework of our studies on Citrus cultivars in Greece, the chemical composition of the essential oils (EOs) from the peels and leaves of orange, pummelo, and tangelo (mandarin × grapefruit hybrid) cultivated in Greece have been studied. All EOs have been analyzed through GC-MS, and a total of 47 and 87 metabolites were identified in the peels and leaves, respectively. These metabolites are classified into the chemical groups of terpenes, alcohols, aldehydes, esters, ketones, and organic acids. Limonene was the most abundant compound in the peel EOs. Moreover, bioactive polymethoxyflavones (PMFs) were isolated and structurally determined from the peels of orange and tangelo, highlighting them as a good potential source of natural PMFs. All EOs were evaluated for their antimicrobial activity against nine human pathogenic microorganisms (six bacteria and three fungi), showing an interesting profile. The EOs from the peels of all Citrus species exhibited a stronger antimicrobial activity compared to those from the leaves. The susceptibility of the assayed Gram-positive bacteria was observed to be greater than that of Gram-negative bacteria, while the fungi were also relatively less resistant than bacteria. The rootstock choice did not influence the EO profile of the fruit peel but exerted an influence on the chemical profile of the leaves.