ὃν ὁ θεὸς ἀνέστησεν λύσας τὰς ὠδῖνας τοῦ θανάτου, καθότι οὐκ ἦν δυνατὸν κρατεῖσθαι αὐτὸν ὑπ' αὐτοῦ·
I would say that the antecedent of the 3rd-person singular pronoun αὐτοῦ is "death" (the articular genitival τοῦ θανάτου). τὰς ὠδῖνας cannot be the antecedent since that noun phrase is accusative plural whereas τοῦ θανάτου is genitive singular. It seems that αὐτοῦ is used anaphorically here (its "normal" use). Cf. Wallace, GGBB, page 324. A good example of an anaphoric personal pronoun is Acts 27:32.
The NRSV has for Acts 2:24: "But God raised him up, having freed him from death, because it was impossible for him to be held in its power" (1989 Version). In the ftn., it has "Gk. pains of death."