Raman spectra of oxacillin (OXN), carbenicillin (CBC), and azlocillin (AZL) are reported for the first time together with their full assignment of the normal modes, as calculated using Density Functional Theory (DFT) methods with the B3LYP exchange-correlation functional coupled to the 6-31G(d) and 6-311+G(2d,p) basis sets. Molecular docking studies were performed on five penicillins, including OXN, CBC, and AZL. Subsequently, their chemical reactivity and correlated efficiency towards specific pathogenic strains were revealed by combining frontier molecular orbital (FMO) data with molecular electrostatic potential (MEP) surfaces. Their bactericidal activity was tested and confirmed on a couple of species, both Gram-positive and Gram-negative, by using the disk diffusion method. Additionally, a surface-enhanced Raman spectroscopy (SERS)—principal component analysis (PCA)-based resistogram of A. hydrophila is proposed as a clinically relevant insight resulting from the synergistic cheminformatics and vibrational study on CBC and AZL.