Essential oils (EOs) with established and well-known activities against human pathogens might become new therapeutics in multidrug-resistant bacterial infections, including respiratory tract infections. The aim of this study was to evaluate the antimicrobial activity of EOs obtained from several samples of Origanum vulgare, O. syriacum, and O. majorana cultivated in Poland. EOs were analyzed by GC-MS and tested against four bacterial strains: Staphylococcus aureus (MRSA), Haemophilus influenzae, Haemophilus parainfluenzae, and Pseudomonas aeruginosa. Chemical analyses showed that the Eos were characterized by a high diversity in composition. Based on the chemical data, four chemotypes of Origanum EOs were confirmed. These were carvacrol, terpineol/sabinene hydrate, caryophyllene oxide, and thymol chemotypes. Thin-layer chromatography-bioautography confirmed the presence of biologically active antibacterial components in all tested EOs. The highest number of active spots were found among EOs with cis-sabinene hydrate as the major compound. On the other hand, the largest spots of inhibition were characteristic to EOs of the carvacrol chemotype. Minimal inhibitory concentrations (MICs) were evaluated for the most active EOs: O. vulgare ‘Hirtum’, O. vulgare ‘Margarita’, O. vulgare ‘Hot & Spicy’, O. majorana, and O. syriacum (I) and (II); it was shown that both Haemophilus strains were the most sensitive with an MIC value of 0.15 mg/mL for all EOs. O. majorana EO was also the most active in the MIC assay and had the highest inhibitory rate in the anti-biofilm assay against all strains. The most characteristic components present in this EO were the trans-sabinene hydrate and terpinen-4-ol. The strain with the least sensitivity was the MRSA with an MIC of 0.6 mg/mL for all EOs except for O. majorana, where the MIC value reached 0.3 mg/mL. Scanning electron microscopy performed on the Haemophilus influenzae and Haemophilus parainfluenzae biofilms showed a visible decrease in the appearance of bacterial clusters under the influence of O. majorana EO.