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abstract: 'We use direct method oxygen abundances in combination with strong optical emission lines, stellar masses (${\hbox{$M_{\star}$}}$), and star formation rates (SFRs) to recalibrate the N2, O3N2, and N2O2 oxygen abundance diagnostics. We stack spectra of $\sim$200,000 star-forming galaxies from the Sloan Digital Sky Survey in bins of ${\hbox{$M_{\star}$}}$ and SFR offset from the star forming main sequence (${\hbox{$\Delta\log$(SSFR)}}$) to measure the weak emission lines needed to apply the direct method. All three new calibrations are reliable to within $\pm 0.10$ dex from $\log({\hbox{$M_{\star}$}}/{M_{\odot}}) \sim 7.5 - 10.5$ and up to at least $200~{M_{\odot}}$ yr$^{-1}$ in SFR. The N2O2 diagnostic is the least subject to systematic biases. We apply the diagnostics to galaxies in the local universe and investigate the $M_{\star}$–$Z$–${\rm SFR}$ relation. The N2 and O3N2 diagnostics suggest the SFR dependence of the $M_{\star}$–$Z$–${\rm SFR}$ relation varies with both ${\hbox{$M_{\star}$}}$ and ${\hbox{$\Delta\log$(SSFR)}}$, whereas the N2O2 diagnostic suggests a nearly constant dependence on SFR. We apply our calibrations to a sample of high redshift galaxies from the literature, and find them to be metal poor relative to local galaxies with similar ${\hbox{$M_{\star}$}}$ and SFR. The calibrations do reproduce direct method abundances of the local analogs. We conclude that the 