  We study theoretically the mixed state properties of a strong
uniaxially-anisotropic type II superconductor with the Pauli paramagnetic
effect, focusing on their behaviors when the magnetic field orientation is
tilted from the conduction layer ab plane. On the basis of Eilenberger theory,
we quantitatively estimate significant contributions of the Pauli paramagnetic
effects on a variety of physical observables, including transverse and
longitudinal components of the flux line lattice form factors, magnetization
curves, Sommerfeld coefficient, field distributions and magnetic torques. We
apply these studies to Sr_2_RuO_4_ and quantitatively explain several seemingly
curious behaviors, including the H_c2_ suppression for the ab plane direction,
the larger anisotropy ratio and intensity found by the spin-flip small angle
neutron scattering, and the first order transition observed recently in
magneto-caloric, specific heat and magnetization measurements in a coherent and
consistent manner. Those lead us to conclude that Sr_2_RuO_4_ is either a
spin-singlet or a spin-triplet pairing with the d-vector components in the ab
plane.
