We introduce the notion of compatibility between a set-valued quasi-metric and the original metric. By using this notion we prove a general set-valued Ekeland's variational principle (EVP), where the perturbation contains a set-valued quasi-metric which is compatible with the original metric. Here, we need not assume that the order cone is w-normal. By using the unified approach for approximate solutions introduced by Gutierrez, Jimenez, and Novo, we deduce a general version of set-valued EVP based on (C, epsilon)-efficient solutions, where C is a coradiant set contained in the order cone. By choosing two specific versions of the coradiant set C in the general version of EVP, we obtain several particular set-valued EVPs for epsilon-efficient solutions in the sense of Nemeth and of Dentcheva and Helbig, respectively. These set-valued EVPs improve and generalize the related interesting results in [C. Gutierrez, B. Jimenez, and V. Novo, SIAM J. Control Optim., 47 (2008), pp. 883-903].