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We revisit our previous work [Phys. Rev. D 95, 096014 (2017)] where neutrino oscillation and nonoscillation data were analyzed in the standard framework with three neutrino families, in order to constrain their absolute masses and to probe their ordering (either normal, NO, or inverted, IO). We include updated oscillation results to discuss best fits and allowed ranges for the two squared mass differences $δm^2$ and $Δm^2$, the three mixing angles $θ_{12}$, $θ_{23}$ and $θ_{13}$, as well as constraints on the CP-violating phase $δ$, plus significant indications in favor of NO vs IO at the level of $Δχ^2=10.0$. We then consider nonoscillation data from beta decay, from neutrinoless double beta decay (if neutrinos are Majorana), and from various cosmological input variants (in the data or the model) leading to results dubbed as default, aggressive, and conservative. In the default option, we obtain from nonoscillation data an extra contribution $Δχ^2 = 2.2$ in favor of NO, and an upper bound on the sum of neutrino masses $Σ< 0.15$ eV at $2σ$; both results - dominated by cosmology - can be strengthened or weakened by using more aggressive or conservative options, respectively. Taking into account such variations, we find that the combination of all (oscillation and nonoscillation) neutrino data favors NO at the level of $3.2-3.7σ$, and that $Σ$ is constrained at the $2σ$ level within $Σ< 0.12-0.69$ eV. The upper edge of this allowed range corresponds to an effective $β$-decay neutrino mass $m_β= Σ/3 = 0.23$ eV, at the sensitivity frontier of the KATRIN experiment.