my guess in how to use it is to use the card after transfers, so Ill be prepared for the big hit, (and survive with luck) and then... counterattack.
You're right on almost everything. Indeed, an OD card makes sure that the other hits you first and then you can counter-attack. But, the AI can play the card too, so what happens if it does?
When both players play an Order delay card, first all the orders before both players' OD card are executed, no matter how many orders each player has before their card. (You can move the card up and down the orders list!)
After all those orders have been executed, the game starts executing the orders after the OD cards for both players. The game does it in the same fashion as if nobody had played the card: A BB AA BB AA B...
So in some situations you might want to take into account that the AI can also play the card and push as many orders below your OD card as possible. In a lot of cases it is worth it to set your OD card as the first move, if you want to make sure you have the last move and can counterattack.
As for the level, i haven't played it so i can only give global advice, rather than specifics. Hope you beat it soon, otherwise PM me :)