  We present a systematic study of the sensitivity of quasielastic
neutrino-nucleus cross sections at intermediate energies to the strange quark
sea of the nucleon. To this end, we investigate the impact of the weak
strangeness form factors on the ratio of proton-to-neutron knockout, the ratio
of neutral-to-charged current cross sections, on the Paschos-Wolfenstein
relation, and on the longitudinal helicity asymmetry. The influence of axial as
well as vector strangeness effects is discussed. For the latter, we introduce
strangeness parameters from various hadron models and from a recent fit to data
from parity violating electron scattering.
  In our model, the nuclear target is described in terms of a relativistic
mean-field approach. The effects of final-state interactions on the outgoing
nucleon are quantified within a relativistic multiple-scattering Glauber
approach. Our results are illustrated with cross sections for the scattering of
1 GeV neutrinos and antineutrinos off a $^{12}$C target.
  Folding with a proposed FINeSSE (anti)neutrino energy-distribution has no
qualitative influence on the overall sensitivity of the cross-section ratios to
strangeness mechanisms. We show that vector strangeness effects are large and
strongly $Q^2$ dependent.
