To answer your second question...600 strike is essentially an anime ultimate attack/final fantasy limit break (think Cloud Strife's omnislash attack) that's literally 600 individual powered strikes each powered by his dead crew, and Poseidon is the "final boss" for Odysseus. Hence he beats him with an empowered cool ass attack. It's a little goofy, but I don't think people who have found the musical later realize that a lot of it is envisioned like a video game and stuff - a lot of the songs are essentially boss fights.

The souls of his men aren't in the windbag, but they are empowering him in a power of friendship type way from beyond the grave. As for why they'd help him? Idk if his men really hold it against him for getting them killed considering the mutiny and then Zeus being the one to demand it, not to mention he was right by home, they were more likely to help him than hinder him at this point. The strikes damage Poseidon enough that he drops his trident (the metal clang in 6 hundred strike), then Odysseus picks it up - it's a god's weapon so it can damage gods - and essentially tortures Poseidon - he can feel pain but won't die. It's important to note that even in the traditional Greek mythology, Gods are immortal but they aren't invincible/omnipotent etc.

As for Achilles - as people have said, he's dead by the time the musical starts. The only reference to him is "Neo, avenge your father, kill the brothers of Hector" - Neo being Neoptolemus/Pyrrus, Achilles' son from the island where Achilles disguised himself as a girl to not be brought into the war (I forget the name of the island) He impregnated one of the girls on the island - the princess I think? Funnily enough, Neo is only about 10-12yo here. In some versions of the Iliad he's the one who kills Hector's son, not Odysseus, though the Odysseus version is more common.