All measurements of cosmic star formation must assume the stellar initial mass function (IMF) to extrapolate from the star-formation rate (SFR) measured for massive stars to the total SFR. Traditional determinations of the IMF in galaxies are made at ultraviolet, optical and near-infrared wavelengths, which cannot be probed in dusty gas-rich galaxies. The 13C/18O abundance ratio in the ISM – which were produced mainly by low-mass stars and massive stars, respectively -- has been demonstrated as a sensitive index of the IMF in gas-rich galaxies.  Besides the 13C/18O ratio, which is associated with different C and O major isotopes, 17O and 18O are likely even better for tracing the IMF slope because of the same root in the oxygen family. Here we present our new ALMA observations and archival data of 17O and 18O in nearby galaxies, covering from low-metallicity dwarf galaxies to gas-rich starburst galaxies. A systematic trend of 17O/18O ratios from starbursts to low-SFR galaxies implies that a variable IMF is inevitable. We will also present our recent 12C/13C benchmarking against our Milky Way, extending to the low-metallicity outer Galactic disk region.