Ionized nebulae provide critical insights into the conditions of the interstellar medium (ISM). Their bright emission lines enable the measurement of physical properties, such as the gas-phase metallicity, across galaxy discs and in distant galaxies. The PHANGS-MUSE survey has produced optical spectroscopic coverage of the central star-forming discs of 19 nearby main-sequence galaxies. Here, we use the Halpha morphology from this data to identify 30790 distinct nebulae, finding thousands of nebulae per galaxy. For each nebula, we extract emission line fluxes and, using diagnostic line ratios, identify the dominant excitation mechanism. A total of 23244 nebulae (75 per cent) are classified as HII regions. The dust attenuation of every nebulae is characterized via the Balmer decrement and we use existing environmental masks to identify their large-scale galactic environment (centre, bar, arm, interarm, and disc). Using strong-line prescriptions, we measure the gas-phase oxygen abundances (metallicity) and ionization parameter for all HII regions. With this new catalogue, we measure the radial metallicity gradients and explore second-order metallicity variations within each galaxy. By quantifying the global scatter in metallicity per galaxy, we find a weak negative correlation with global star formation rate and stronger negative correlation with global gas velocity dispersion (in both ionized and molecular gas). With this paper we release the full catalogue of strong line fluxes and derived properties, providing a rich data base for a broad variety of ISM studies.