This paper investigates the complex physical phenomenon of oblique drop impact on superhydrophobic substrates with two-tier roughness (patterned with varied submillimeter-scale posts and coated with nanoparticles). Experimental results show that the impact Weber number of drops and the solid fraction of the submillimeter-scale post structures are crucial for the outcomes of oblique drop collisions. Water droplets with 10 < We(n) < 245 are found to rebound on all the test substrates. As the surface solid fraction decreases, four possible bouncing patterns occur in sequence: sliding rebound, stretched rebound, penetration rebound, and breakup rebound. We demonstrate that the stretched rebound, in which the drops bounce off the surface rapidly in an elongated shape without tangential retraction, allows a 10%similar to 30% reduction of contact time compared with conventional sliding rebound on oblique surfaces. Three types of stretched rebound are observed on substrates with moderate solid fraction (0.1 < phi < 0.5), in which the liquid detachment starts from front, center, and tail, respectively. A simple analytical argument is presented to explain the occurrence of distinct patterns. These findings are believed to provide valuable guidance to the design of self-cleaning and anti icing surfaces under oblique liquid impacts where rapid drop shedding is profitable.