most of the moves you can learn them by having certain bonds with certain characters if i remember correctly Grand fire you need 100% with goenji,toramaru and hiroto all of them in inazuma japan version(i dont know how it's called here) and god catch you need 100% with the 3 endous or mark i think
Jet Stream is a combination between 3 of Inazuma National/Japan's players: Mark (needed) plus two of the following: Axel, Austin Hobbes (and Caleb Stonewall). I unlocked using the first three but I imagine you could substitute either Axel or Hobbes with Stonewall although I did not check this at the time. You need 100% bond between all combinations of three players including Mark.
I used a really old thread here to check for possible moves as a starting point: http://www.gamefaqs.com/boards/998124-inazuma-eleven-strikers/59754491
If some of the names and moves are hard to understand, you might need to research into the anime to make some sense of it.
Fastest way still seems to be to play matches with them in and concentrate on making passes between the players you want to build up. I place the players into a triangle within the formation. The least useful part of the formation are the strikers, because there is not a way to force a regular pass instead of a through pass. For the team, I would throw as many players to unlock moves into the formation. Players that unlock more than one move with players in the formation should take up a more central position. It still takes forever, though, but at least I was unlocking multiple moves in some matches.
The Last Story: ROOK7 (PAL) http://www.youtube.com/user/guestface
Imo the fastest way to raise bonds is completing tournaments. This way you win stats boosters too, very useful for winning friendly matches with platinum.
If you are interested in raising bonds for 2 or 3 people only you can use training. If you continue to hit that tree and the ball touches the ground not even once, you earn like 20% of bonds. At first it's a bit difficult, but not so much.
Ah, and that old thread is... old. I just did a guide for strikers pal: http://watashiwa7.altervista.org/ie/strikers/strikers_en.htm