Here's the thing. To the best of my knowledge, only one of those games takes place after Kingdom Hearts 2. Dream Drop Distance, if I recall correctly, was the only one that continued the story. I don't own a 3DS, so I can't say for sure, so I'm not really going to touch on that. Those other three though...
Re:coded added nothing. It was basically a retelling of Kingdom Hearts or something like that. Same worlds, same characters, same plot on a lot of those worlds. Sora got trapped in a computer if I remember right, or it was an A.I. of him. At least, I think so. I never played that one either, but I know that it didn't continue the story, or really even expand on it.
358/2 days does not take place after Kingdom Hearts 2. In fact, it's a prequel to that game. It tells the story of Roxas and how he came to join Organization XIII, became friends with Axel and Xion, and ended up being captured by Riku and thrown into that VR that he's in at the start of Kingdom Hearts 2. It expands on that extended cut ending in Kingdom Hearts, but it does not continue the main storyline. It's a side story that you can safely skip unless you want to know more about Roxas. I personally enjoyed the game myself, but it was much like Chain of Memories: in between and fills in small story points, but nothing too major.
Birth By Sleep is a prequel. I own the game, but haven't gotten around to playing it yet. However, I do know that it takes place before Kingdom Hearts and sets up the events that lead into the first game, such as the 'soul' that Sora and Roxas share.
So, none of those games take place between 2 and 3, except maybe the first two. You can bet though that they aren't major stories, but little side notes. That's why the fans are so excited about an actual Kingdom Hearts 3 game. It will finally continue the main storyline instead of rehashing old ideas and characters and telling stories that, while interesting, don't actually move the plot along. It's like getting fun DLC packs for a game (like Mass Effect 2), versus getting the next actual game in the series (like finally releasing Mass Effect 3).
As for what they'll do with all this story, I think it's going to be set on the shelf. There may be some call backs here and there--a cameo, or a name drop in a sentence--but I'm betting that this is going to be the start of a whole new adventure. Remember, there were call backs in Kingdom Hearts 2 to Chain of Memories, but the game didn't waste any time trying to catch you up on CoM's events beyond a little blurb in the journal.