Searching for energetic materials with balanced detonation performance and sensitivity is a long-standing goal in the development of high energy density materials (HEDMs). In this work, density functional theory calculations are carried out to characterize the structure-property relationships of four linked 1,2,4-oxadiazole/1,2,4-oxadiazole and 1,2,4-oxadiazole/1,3,4-oxadiazole derivatives. Our results show that all these designed compounds possess good oxygen balance, positive heats of formation, high crystal densities, remarkable detonation performance, and acceptable impact sensitivity. Particularly, the first of these compounds has the best balanced detonation performance and sensitivity, with excellent detonation performance superior to that of 1,3,5-trinitro-1,3,5-triazinane (RDX) and lower impact sensitivity than that of 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX). Given these exceptional properties, it is expected that all these designed compounds are potential HEDM candidates with low sensitivity.