I'm currentlt still reading the novels, but the illustrations mainly the one with the multiple heads makes me wonder if imagine Breaker isn't one ability but several mainly different levels or forms of negation. Touma thinks that the dragon that could win againt the World Rejector couldn't be the same as the one that lost to Othinus a Magic God a being that could be easily erased by World Rejector. (In Shinyaku Toaru Majutsu no Index Light Novel Volume 15)
Index mentions the it's able to negate God's blessings and the red string of fate. But he can't negate the Power of the World. If find the strange because he can negate luck and the red string. Which are natural things or at least thats what I'm assuming
According to the Phase page, the sparks produced by phase collisions can be considered luck, and IB can protect against these to some extent. Though there is indeed no evidence for a red string of fate.
If you have read New Testament 18 then you would find the conversation between Aleister Crowley and Kamijou Touma where the former speaks to the latter about the origin of Imagine Breaker and Academy City.
Imagine Breaker represents all the hopes and dreams of the magicians who wish to return or revert back to the Original World or Phase. It is basically a failsafe measure.
Like for example, your computer is going through a period of slow down. Thus of course you want to revert your computer systems to an earlier state. So you specify the date and time based upon which your computer would be reset to an earlier period of state.
Just like that the Imagine Breaker works to revert back the state of the World or a Phase to an earlier format.
The negation caused by Imagine Breaker when it comes into contact with the supernatural like the Esper Powers and the Magical Powers is actually it's side effect and not it's original purpose.
So the entire series is based on the side effect caused by the Imagine Breaker's host i.e. Kamijou Touma.
Also Imagine Breaker did not specifically choose Kamijou Touma. Throughout history the Imagine Breaker kept changing it's host between either living things (like the Saint before Kamijou Touma who was it's previous host) to non living things like a hand mirror of a staff.
Thus it randomly ended up in Kamijou Touma's right hand. But it was an absolute power whose actual usage is still not mentioned in the story. But Terra of the Left and Aleister Crowley did know specific secrets along with Ollerus and Othinus. Therefore Aleister Crowley wanted the Imagine Breaker into his possession.
How? He specifically knew where the next host will be born (in Japan) and his name (Kamijou Touma) and his personality (saving people to bring a smile), based upon these he created Academy City.
If Touma-kun was a boxer then Academy City would be creating boxers.
If Touma-kun was an Athlete then Academy City would be creating Athletes.
If Toum-kun was a cook then Academy City would host cooking competitions.
But here Touma-kun uses his fists to save people and thus Academy City created Espers.
So if we observe everything as Gods we get to know that all kinds of Incidents like the Sisters, Clone Dolly, Level 6 Shift, the Level 5s', Battle Royale, Roman Catholic, World War III, Gremlin, World Rejector and all other conflicts occured because of Kamijou Touma himself.
Though not his fault but his naive thinking of what his actions would do in the future led to the other powers take advantage of him and create these incidents. So he is not to be blamed for these. The Imagine Breaker is what many people need but the host is the one who truly represents Imagine Breaker.
Kamijou Touma is the one who represents Imagine Breaker. Even without Imagine Breaker he would still fight. (Like in New Testament 22) So this is Imagine Breaker's significance.
Now about the dragons...
One Dragon Head comes out when facing a magician. (fighting Aureolus Izzard)
Eight Dragon Heads comes out when facing a esper power at borderline Level 6. (fighting Misaka Mikoto)
(Read the Railgun Manga Chapter 69)
Some red colured polygon structures comes out in New Testament 22 ending even I do not have any idea of.
Thus our best way to get accurate information is to kidnap 'Kazuma Kamachi' and force him to do three things which I want... whether he likes it or not.
1. The Secrets of his Right Hand (Everything including Imagine Breaker and the Dragons)
2. His Past Story with 'Kumokawa Seria' and 'Mitsuari Ayu'. (Shokuhou Misaki's story was shown in NT 11)
3. Continue 'Toaru Majutsu no Index' light novels for another 15 years. Or else...
It's still not clear exactly Imagine Breaker is. In NT22, even Coronzon admits to not fully understanding how it works. The use of Imagine Breaker to return the world to a previous state only confirms that it can be used in this way, not that this is its intended purpose.