The JLA's first trip to the universe is where Owlman is found hacking computer systems to get the info he needs. There, the JLA fights recruits the Crime Syndicate of America has recruited. Their second trip was when Batman followed Superwoman, and defeats her. After taking out Superwoman, he calls the JLA, and alongside the JLA travels to the moon, to get to the Crime Syndicate's headquarters. From there on, every JLA'er fights against their counterparts, and Wonder Woman manages to even win against her counterpart, Superwoman.
Wonder Woman, Hermes and Zola is at a café where a guy called Lennox, who knew that Zola is pregnant with Zeus and who Wonder Woman and Hermes really is arrived there, and tells to Wonder Woman that he is Diana’s brother. He tells to Diana that she has to be at the London Bridge at six, or she’d regret it. She’s there at six, and Poseidon arrives, and tells Diana that he wants to be the new god of the gods, whereas Lennox goes into a cave shown to him by Hermes, and there he meets Hades who also wants to claim the throne of the Heavens. After Hera arrives, Wonder Woman tricks all of them, and Hades goes back into his cave, and tricks Zola to come to him and kidnap her, he told Diana that they struck a bargain, and when she has fulfilled her’s, she shall get Zola back.
Wonder Woman (vol. 1) #105 revealed that Diana was formed from clay by the Queen of the Amazons, given life and power by four of the Greek and Roman gods (otherwise known as the Olympian deities) as gifts, corresponding to her renowned epithet: "Beautiful as Aphrodite, wise as Athena, swifter than Hermes, and stronger than Hercules", making her the strongest of the Amazons. Wonder Woman's Amazon training gave her limited telepathy, profound scientific knowledge, and the ability to speak every language – even caveman and Martian languages.
Hermes Action Comics #267 (August 1960) Hermes is the Messenger of the Gods, and the God of Thievery, Speed, Travel, and Commerce who is based on the god of the same name. Post-Crisis, Hermes was one of Wonder Woman's earliest allies. He was eventually killed by Circe during the War of the Gods, but Wonder Woman freed him much later from Tartarus. In the New 52, the bird-like Hermes was a close ally to Wonder Woman and aided in protecting Zeke, the reincarnation of Zeus. Post-Rebirth, Hermes took the form of a tortoise and aided Wonder Woman alongside several other gods.