We use solar spectra obtained by the Ozone Monitoring Instrument (OMI) on board the Aura satellite to detect and follow long-term (years) and short-term (weeks) changes in the solar spectral irradiance (SSI) in the 265-500 nm spectral range. During solar Cycle 24, in the relatively line-free regions the SSI changed by ~0.6%+/-0.2% around 265 nm. These changes gradually diminish to 0.15%+/-0.20% at 500 nm. All strong spectral lines and blends, with the notable exception of the upper Balmer lines, vary in unison with the solar "continuum." Besides the lines with strong chromospheric components, the most involved species include Fe I blends and all prominent CH, NH, and CN spectral bands. Following the general trend seen in the solar "continuum," the variability of spectral lines also decreases toward longer wavelengths. The long-term solar cycle SSI changes are closely, to within the quoted 0.1%-0.2% uncertainties, matched by the appropriately adjusted short-term SSI variations derived from the 27 day rotational modulation cycles. This further strengthens and broadens the prevailing notion about the general scalability of the UV SSI variability to the emissivity changes in the Mg II 280 nm doublet on timescales from weeks to years. We also detect subtle deviations from this general rule: the prominent spectral lines and blends at {lambda} >~ 350 nm show slightly more pronounced 27 day SSI changes when compared to the long-term (years) trends. We merge the solar data from Cycle 21 with the current Cycle 24 OMI and GOME-2 observations and provide normalized SSI variations for the 170-795 nm spectral region.