  Main Sequence Turn-off stars (MSTO) and subgiant stars are good tracers of
galactic populations. We present a study of 41,034 MSTO and subgiant stars from
the GALAH survey. Using a grid of stellar models that accounts for the
variation of O abundances, we determine their ages with a median age
uncertainty of $\sim$9.4 per cent. Our analysis reveals that the ages of high-O
stars based on O-enhanced models (OEM models) are smaller than those determined
with $\alpha$-enhanced models, resulting in a mean fractional age difference of
-5.3 per cent at [O/$\alpha$] = 0.2 and -11.0 per cent at [O/$\alpha$] = 0.4.
This age difference significantly impacts the age distribution of thick disc
and halo stars, leading to a steeper downward trend in the [Fe/H]-age plane
from 8 Gyr to 14 Gyr, indicating a shorter formation time-scale and a faster
chemical-enhanced history for these populations. We confirm the V-shape of the
normalized age-metallicity distribution $p$($\tau$$\mid$[Fe/H]) of thin disc
stars, which is presumably a consequence of the second gas infall.
Additionally, we find that the halo stars in our sample can be divided into two
sequences, a metal-rich sequence (Splash stars) and a metal-poor sequence
(accreted stars), with the Splash stars predominantly older than 9 Gyr and the
accreted halo stars older than 10 Gyr. Finally, we observe two distinct
sequences in the relations between various chemical abundances and age for disc
stars, namely a young sequence with ages $<$ $\sim$8 Gyr and an old sequence
with ages $>$ $\sim$8 Gyr.
