Efficient implementations of the orbital-optimized MP3 and MP2.5 methods with the density-fitting (DF-OMP3 and DF-OMP2.5) and Cholesky decomposition (CD-OMP3 and CD-OMP2.5) approaches are presented. The DF/CD-OMP3 and DF/CD-OMP2.5 methods are applied to a set of alkanes to compare the computational cost with the conventional orbital-optimized MP3 (OMP3) [Bozkaya J. Chem. Phys. 2011, 135, 224103] and the orbital-optimized MP2.5 (OMP2.5) [Bozkaya and Sherrill J. Chem. Phys. 2014, 141, 204105]. Our results demonstrate that the DF-OMP3 and DF-OMP2.5, methods provide considerably lower computational costs than OMP3 and OMP2.5. Further application results show that the orbital-optimized methods are very helpful for the study of open-shell noncovalent interactions, aromatic bond dissociation energies, and hydrogen transfer reactions. We conclude that the DF-OMP3 and DF-OMP2.5 methods are very promising for molecular systems with challenging electronic structures.