The properties of micromechanically exfoliated graphene on different oxide dielectrics--SiO(2), Al(2)O(3), and HfO(2)--are investigated by Raman spectroscopy and AFM measurement. The pristine graphene has stronger adhesion and a higher hole concentration when the dielectric constant of the underlying oxide is higher. It is found that annealing under a high vacuum significantly enhances the adhesion between graphene and the oxides and causes a shift of the Raman G and 2D bands to a higher wavelength. The high vacuum annealing also causes an increase in carrier concentration of up to ten times with a corresponding Fermi level shift of approximately 0.65 eV for graphene on HfO(2). On the other hand, the high vacuum annealing of graphene on SiO(2) induces a biaxial compressive stress as high as 4 GPa on graphene. The results provide understanding on the interaction of graphene and oxides, which is essential for successful realization of graphene-based electronic devices.