  We characterize the metallicities and physical properties of cool,
photoionized gas in a sample of 152 z<1 strong Lya forest systems (SLFSs,
absorbers with 15<log N(HI)<16.2). The sample is drawn from our COS
circumgalactic medium (CGM) compendium (CCC), an ultraviolet survey of
HI-selected circumgalactic gas around z<1 galaxies that targets 262 absorbers
with 15<log N(HI)<19. We show that the metallicity probability distribution
function of the SLFSs at z<1 is unimodal, skewed to low metallicities with a
mean and median of [X/H]=-1.47$ and -1.18 dex. Very metal-poor gas with
[X/H]<-1.4 represents about half of the population of absorbers with 15<log
N(HI)<18. Thus, there are important reservoirs of primitive (though not
pristine) gas around z<1 galaxies. The photoionized gas around z<1 galaxies is
highly inhomogeneous based on the wide range of metallicities observed
(-3<[X/H]<+0.4) and that there are large metallicity variations (factors of 2
to 25) for most of the closely-spaced absorbers (Dv<300 km/s) along the same
sightlines. These absorbers show a complex evolution with redshift and HI
column density, and we identify subtle cosmic evolution effects that affect the
interpretation of metallicity distributions and comparison with other of
absorbers samples. We discuss the physical conditions and cosmic baryon and
metal budgets of the CCC absorbers. Finally, we compare the CCC results to
recent cosmological zoom simulations and explore the origins of the 15<log
N(HI)<19 absorbers within the EAGLE high-resolution simulations.
