Despite numerous studies the exact nature of the order parameter in superconducting Sr2RuO4 remains unresolved. We have extended previous small-angle neutron scattering studies of the vortex lattice in this material to a wider field range, higher temperatures, and with the field applied close to both the ⟨100⟩ and ⟨110⟩ basal plane directions. Measurements at high field were made possible by the use of both spin polarization and analysis to improve the signal-to-noise ratio. Rotating the field towards the basal plane causes a distortion of the square vortex lattice observed for H∥⟨001⟩ and also a symmetry change to a distorted triangular symmetry for fields close to ⟨100⟩. The vortex lattice distortion allows us to determine the intrinsic superconducting anisotropy between the c axis and the Ru-O basal plane, yielding a value of ∼60 at low temperature and low to intermediate fields. This greatly exceeds the upper critical field anisotropy of ∼20 at low temperature, reminiscent of Pauli limiting. Indirect evidence for Pauli paramagnetic effects on the unpaired quasiparticles in the vortex cores are observed, but a direct detection lies below the measurement sensitivity. The superconducting anisotropy is found to be independent of temperature but increases for fields ≳1 T, indicating multiband superconductvity in Sr2RuO4. Finally, the temperature dependence of the scattered intensity provides further support for gap nodes or deep minima in the superconducting gap.