Emergence of antibiotic-resistant bacteria is a serious threat to the public health. This is also true for Staphylococcus aureus and other staphylococci. Staphylococcus phages Stab20, Stab21, Stab22, and Stab23, were isolated in Albania. Based on genomic and phylogenetic analysis, they were classified to genus Kayvirus of the subfamily Twortvirinae. In this work, we describe the in-depth characterization of the phages that electron microscopy confirmed to be myoviruses. These phages showed tolerance to pH range of 5.4 to 9.4, to maximum UV radiation energy of 25 µJ/cm², to temperatures up to 45 °C, and to ethanol concentrations up to 25%, and complete resistance to chloroform. The adsorption rate constants of the phages ranged between 1.0 × 10⁻⁹ mL/min and 4.7 × 10⁻⁹ mL/min, and the burst size was from 42 to 130 plaque-forming units. The phages Stab20, 21, 22, and 23, originally isolated using Staphylococcus xylosus as a host, demonstrated varied host ranges among different Staphylococcus strains suggesting that they could be included in cocktail formulations for therapeutic or bio-control purpose. Phage particle proteomes, consisting on average of ca 60–70 gene products, revealed, in addition to straight-forward structural proteins, also the presence of enzymes such DNA polymerase, helicases, recombinases, exonucleases, and RNA ligase polymer. They are likely to be injected into the bacteria along with the genomic DNA to take over the host metabolism as soon as possible after infection.