  We present optical-line gas metallicity diagnostics established by the
combination of local SDSS galaxies and the largest compilation of extremely
metal-poor galaxies (EMPGs) including new EMPGs identified by the Subaru
EMPRESS survey. A total of 103 EMPGs are included that cover a large parameter
space of magnitude (Mi=-19 to -7) and H-beta equivalent width (10-600 Ang),
i.e., wide ranges of stellar mass and star-formation rate. Using reliable
metallicity measurements of the direct method for these galaxies, we derive the
relationships between strong optical-line ratios and gas-phase metallicity over
the range of 12+log(O/H)=~6.9-8.9 corresponding to 0.02-2 solar metallicity
Zsun. We confirm that R23-index, ([OIII]+[OII])/H-beta, is the most accurate
metallicity indicator with the metallicity uncertainty of 0.14 dex over the
range among various popular metallicity indicators. The other metallicity
indicators show large scatters in the metal-poor range (<0.1 Zsun). It is
explained by our CLOUDY photoionization modeling that, unlike R23-index, the
other metallicity indicators do not use a sum of singly and doubly ionized
lines and cannot trace both low and high ionization gas. We find that the
accuracy of the metallicity indicators is significantly improved, if one uses
H-beta equivalent width measurements that tightly correlate with ionization
states. In this work, we also present the relation of physical properties with
UV-continuum slope beta and ionization production rate xi_ion derived with
GALEX data for the EMPGs, and provide local anchors of galaxy properties
together with the optical-line metallicity indicators that are available in the
form of ASCII table and useful for forthcoming JWST spectroscopic studies.
