Orbital degree of freedom plays an important role in understanding exotic phenomena of strongly correlated materials. We study strongly correlated ultracold bosonic gases coupled to a high-finesse cavity, pumped by a blue-detuned laser in the transverse direction. Based on an extended Bose-Hubbard model with parameters adapted to recent experiments, we find that by tuning the reflection of pump laser, atoms can be selectively transferred to the odd-parity p-orbital, or to even-parity d-orbital band of a two-dimensional square lattice, accompanied with cavity-photon excitations. By interacting with cavity field, atoms self-organize to form stable higher-orbital superfluid and Mottinsulating phases with orbital-density waves, as a result of cavity induced orbital-flip processes. Our study opens the route to manipulate orbital degrees of freedom in strongly correlated quantum gases via coupling to optical cavities.