LiTi2O4 is a unique compound in that it is the only known spinel oxide superconductor. The lack of high quality single crystals has thus far prevented systematic investigations of its transport properties. Here we report a careful study of transport and tunnelling spectroscopy in epitaxial LiTi2O4 thin films. An unusual magnetoresistance is observed which changes from nearly isotropic negative to prominently anisotropic positive as the temperature is decreased. We present evidence that shows that the negative magnetoresistance likely stems from the suppression of local spin fluctuations or spin-orbit scattering centres. The positive magnetoresistance suggests the presence of an orbital-related state, also supported by the fact that the superconducting energy gap decreases as a quadratic function of magnetic field. These observations indicate that the spin-orbital fluctuations play an important role in LiTi2O4 in a manner similar to high-temperature superconductors.