The game you are describing is more similar to Three Men's Morris than to Tic Tac Toe. Unlike Three Men's Morris, the extra movement options under the rules you cite mean the game is likely a draw under optimal play. I'm assuming that this game has something akin to Chess's draw due to Threefold Repition; if not, the optimal result of the game is that you play forever, in which case the only winning move is not to play.
The classic Three Men's Morris was solved in the 1200's as a first player victory. The Libro de los Juegos lists the following solutions (translation from here):
There are two possible victories, depending upon the second player's moves, the first being: 1. b2, a3; 2. b1, b3; 3. c3, a1; 4. b1-c1, any; 5. b2-c2. The second is 1. b2, b3; 2. a1, c3; 3. a3, a2; 4. a1-b1, any; 5. b1-c1.
Those solutions give a good starting point for this game. I'm going to gloss over a lot of the piece orientations during setup; in general, the optimal piece orientation is implied by the subsequent moves a player wants to threaten.
As player 1, you want to start in the middle with your piece orthogonal (B2+).
Case 1: If player 2 responds in the middle of a side (say B3), player 1 can force a win by playing 2. a1, c3; 3. a3, a2. This generates the following board, where player 1 can move a1-c1 to win:
1 2 3
A X O X
B . X O
C . . O
If player 2 instead plays C1 on turn 3, player 1 can move b2-a2 to win.
Given that, player 2 should respond by playing in a corner (say A3). Player 1 can then force either of the following boards:
Case 2 (1. b2, a3; 2. b1, b3; 3. c3, a1):
1 2 3
A O . O
B X X O
C . . X
This seems to be a draw. Unlike in Three Man's Morris, here Player 1 must move to a2 to prevent a loss (player 2 threatens b3-a2). b1-a2 is the best move as it threatens a player 1 win, but player 2 just responds with b3-c2. Player 1 would then move a2-b1, player 2 would move c2-b3, and the game would be a stalemate.
Case 3 (1. b2, a3; 2. a2, c2; 3. c3, a1):
1 2 3
A O X O
B . X .
C . O X
I can't see any way player 1 can force a win here. If player 1 moves c3-b3 to threaten a win, player 2 moves a1-b1 to block, and the players would then reverse those moves causing a stalemate. Anything else isn't moving towards a victory. I believe this case is a draw as well.