We don't know the masses of the neutrino flavors, just because the neutrino flavors are a combination of neutrino mass eigenstates. A mean value would only make sense. The straightforward searches are based on Tritium, Pion and Tau weak decays. They all can give limits. Of course there are other means that can give lower limits, such as cosmological observations...
As for the mass eigenstates, we still don't know their hierarchy... The difference of mass squared measured by the neutrino oscillation hasn't given us an insight of what is the lowest and highest mass (that's why when people give the mass eigenstates in presentations, they draw two diagrams, the one inversed to the other)
From reading around it seems the upper limit is in the range 0.3 to 2.4eV depending on which measurement method you favor. From the delta mass squared result we have a lower bound of at least one neutrino >= 0.04eV mass.