Basicity depends upon the availability of lone pair of electrons for donation. Between H2O and CH3OH, the later is more basic because of the presence of electron donating −CH3 group.
Thus, CH3OH>H2O (basicity order)
Conjugate base of weaker acid is strong.
Thus, CH3O−>OH−(basicity order)
Hence, the increasing order of basicity is CH3O−>OH−>CH3OH>H2O