Percy Jackson! I had a really weird role-playing stint in that department. Though I thought the books were interesting, especially when it helped me ace a Greek Gods test.
Your story has a sound basis, in the plot anyway. It follows the story of Jacob and his involvement with WWII, which you also incorporated the demigods into. That's a pretty good mix there. Though, I had a problem with the prologue. It was kind of pointless. I'll probably eat those words once Jacob appears in their time. I had to say it though.
Your sentences have a lot of fragments in it. There are a few spelling errors too, but I'll mention those later as we go along. See, you conjoin so many clauses and put it into one sentence. They clog up and you try to nullify it by putting in commas here and there. Those commas are comma splices, and are grammatically incorrect. When you have two independent clauses, you separate them by a semi-colon. For example:
This bit of action could have been used for something for interesting. Say, you could have introduced character with each action. Jacob could have been obviously winning, telling readers that he's a good swordsman or Erik sucks. Also, you didn't use many pronouns. That's alright I guess, but just using their names gets on my nerves. It sure does avoid confusion, though it's annoying. Try to mix it up.
After the second sentence, you're missing a period. Next, yes they sweat, but I don't think drenched is a good word. When I think drenched, I think someone poured it on them. And pouring sweat is absolutely disgusting. Try soaked or, "Sweat patches creeped on their cotton shirts." Okay, a few more things. You describe what they wear, but it was almost excessive. You could have just said they wore armor and be done with it. Listing out what they wear is a tad bit too much.
Okay, two more things! You spelled "plumed" wrong. And you also spelled "warrior" wrong. It's weird because you spelled warrior right later on, so I'm guessing that it was a typo. Done talking about this paragraph!
Okay next part and then I really don't want to say anymore. You transitioned from the Camp back to the past. Jacob's past. It's nifty, but it jumps too quickly. Usually writers do a page break or the characters talk about the event, but you just dive straight into it. I don't like that kind of narrative. It can be fine, but it really takes away from what you're presenting here. Actually, it's best not to mention their pasts until later. I noticed that a lot of role-plays have that bit on characters and their sign-ups, but in genuine writing, it's best to slowly reveal the layers of their past like an onion. Peel off one skin at a time and eventually it'll become clear. You can probably find this most evident in the actual books. I'm talking about the second one where Annabeth has her past revealed and why she doesn't like Tyson.
Make sure the pacing is well balanced. Too slow, and it gets boring. Too fast, and readers get pissed. But just enough and it's interesting.
Gah, I sound like I have no soul. That's okay though. You have a few things to work on, but other than that, I think it's an interesting story. Your style works in beats and it kind of threw me off at first, but I got used to it eventually. Try to mix things up. Your dialogue, at times, didn't sound really human. You'll learn that later. I would highly suggest you proofread your work, both for errors and spelling and such. It's annoying to see typos, especially when the rest of the story is solid. It shows that you're a bit lazy.
Anyway, you have the potential to make this a great story, you just have to work a bit. Then again, you have to work for everything. Keep writing, keep improving, and good luck!