Nightwing will likely draw on his memories of past encounters with the Joker and his training with Batman. He'll keep his cool as much as possible, suppressing any fear or panic. His main goal will be to stay alive until he can either escape on his own or be rescued. He may also try to leave some kind of clue for his rescuers if he can.
Nightwing would initially be defiant. He's a highly trained fighter and detective in his own right. So, he won't cower in front of the Joker. He'll probably try to size up the situation, looking for any weaknesses in his captivity and the Joker's plan.
He might try to engage Slade in conversation. Nightwing is smart and could be looking for a way to psychologically get an edge over Slade. He could be probing for Slade's motives, hoping to find a way to turn the situation around. He might also be stalling for time, waiting for the right moment to make his move.
In the fanfiction, Nightwing could be used by the Joker as bait to lure Batman into a trap. The Joker might have some elaborate and sadistic plan in store for both of them. Nightwing, being the strong - willed character he is, will likely try to resist the Joker's psychological games and attempts to break him while waiting for rescue.
Another possibility is that it's a group of mercenaries hired by a powerful underworld figure. The figure might want Nightwing out of the way so they can carry out their illegal activities more easily. The mercenaries would be well - trained and equipped, making it a difficult situation for Nightwing to escape from.
One possible scenario could be that Nightwing is kidnapped by a new supervillain who wants to use him as bait to lure Batman. The villain might hold Nightwing in an abandoned warehouse, setting up various traps. Another could be that a criminal organization kidnaps him to extract information about the other heroes in Gotham. They might use high - tech devices to try and break his will.
It's also possible that Nightwing and Slade end up having a long conversation during the captivity. Slade might try to convince Nightwing to join his side, perhaps by appealing to some sense of justice that he thinks Nightwing is missing. Nightwing, of course, would resist, but this could lead to some interesting character development for both of them as they debate their different ideologies.
Some Avengers might be excited. Captain America, for example, would probably welcome Nightwing for his sense of justice and fighting skills. Thor might be intrigued by this new addition from another world (in a sense, as Gotham is different from Asgard). However, Hulk might not care much as long as Nightwing doesn't get in his way during a fight. Overall, there would be a mix of curiosity and acceptance.
Batman might become more brooding. He could withdraw from the people around him, like Robin or Commissioner Gordon.
He might try to reason with kaldur. If Nightwing can make kaldur see that what he's doing is wrong or that there are better ways to achieve his goals, kaldur could let him go. Nightwing is known for his charisma and intelligence in such situations.
His motivation could be related to a difference in ideology. Red Hood has a more brutal approach to crime - fighting compared to Nightwing. He might think that Nightwing's methods are too soft and by kidnapping him, he wants to force Nightwing to see things his way.
One possibility is that Red Hood has some sort of vendetta against Nightwing. Maybe he blames Nightwing for something that happened in the past, like a mission gone wrong that affected someone close to Red Hood. So he kidnaps Nightwing to get revenge or to make him pay in some way.