Antimicrobial resistance (AMR) is a global public health problem, and the rapid rise in AMR is attributed to the inappropriate and/or overuse of antibiotics. Therefore, alternative antimicrobial agents, including those of natural origin, are being sought for the development of new drugs. The purpose of our study was to analyze the chemical composition, and antimicrobial and antioxidant activities of four oregano essential oils (OEOs) from Poland, Europe, Turkey and the USA. The antimicrobial activity (AMA) was evaluated using 23 strains, including Gram-positive bacteria, Gram-negative bacteria and Candida species. The antioxidant activity (AA) of essential oils (EOs) was determined by the DPPH method. The main component of the EOs tested was carvacrol (76.64–85.70%). The highest amount of this compound was determined in the Polish OEO. The OEOs we tested showed antimicrobial resistance, which was especially strong against fungi (MIC = 0.06–0.25 mg/mL−1). These products also showed high AA (71.42–80.44%). OEOs high in carvacrol should be the subject of further research as potential antimicrobial and antioxidant agents.