In this study, we determined the antimicrobial activity of ten essential oils (EOs)—oregano, thyme, clove, arborvitae, cassia, lemongrass, melaleuca, eucalyptus, lavender, and clary sage—against drug-resistant microorganisms previously isolated from patients with skin infections. The essential oil compositions were determined using gas chromatography coupled to mass spectrometry (GC/MS). The assayed bacteria included Pseudomonas aeruginosa, Proteus vulgaris, Citrobacter koseri, and Klebsiella pneumoniae. Two drug-resistant yeasts (Candida albicans and Candida parapsilosis) were also involved in our survey. Oregano, thyme, cassia, lemongrass and arborvitae showed very strong antibacterial and antifungal activity against all tested strains. These results show that these essential oils may be effective in preventing the growth of the drug-resistant microorganisms responsible for wound infections. In this study, the genotoxic effects of tested essential oils on healthy human keratinocytes HaCaT were evaluated using the comet assay for the first time. These results revealed that none of the essential oils induced significant DNA damage in vitro after 24 h. Moreover, the treatment of HaCaT cells with essential oils increased the total antioxidant status (TAS) level. The obtained results indicate that EOs could be used as a potential source of safe and potent natural antimicrobial and antioxidant agents in the pharmaceutical and food industries.