Well, since I would be remiss to not jump in on delving into the fighting styles of my other characters...
Gogonji Gegenji:
If Gogon had his way? He wouldn't fight. Not to say that he's a pacifist like his little brother, but more that he excels in the position of being a tactician. He's at his best reading enemy movements and directing his own. He's the "Tactician" character that gives units directions in Fire Emblem - directing his forces to victory while not actually taking the field himself.
Should he be forced to fight for himself, though, he has his tricks though he's not as grand a threat as he was once in the past (he was the Big Bad of a story arc, after all!). He was once a lot stronger then, utilizing experimental magitek devices to force synchronicity with soul crystals and drawing on both the knowledge and the power locked within those shiny stones to cause havoc on the battlefield. However, he had all that ripped from him, went into a coma, and he's still recovering even a good year and a half to two years later. Now he only really his his Arcanima to rely on, which - while decently formidable - is still not as great a skill set compared to artificially-gifted multi-job mastery.
Anyway, his delving into the mathemagical leans heavily on the basics and the Scholastic abilities of Nym. That, along with his analytical approach to combat, means he goes for attempting to read the opponent and developing an appropriate assault tactic. Until that point, he tends to focus on misdirection, enfeeblement, and bolstering his own defenses. Once he finds that chink in his opponent's armor, however, he will strike with surgical precision.
To aid in that, he's also been delving into the Allagan Summoning arts - albeit at a more restricted level due to its requirements. The primal essences needed to summon Egi were "stolen" from a Summoner soul crystal during his earlier escapades, but he has all but the tracest amounts of it at this point after the burnout. If he focuses, he can maintain a single egi but cannot Trance or do any of the higher level abilities. To get around this, his preferred method to use his egis is more of a fighting game striker assist angle. They manifest, attack, and then immediately dissipate - which also helps from a disorientation angle as well.
Should all that fail or he's dealing with someone with incredible aetheric resistances? He's not above the simple solutions. His cane - the need for which is purposely over-inflated to misdirect his enemies even before a fight begins - is a little bag of tricks. The grip has a gem in it that he can use as an added aetheric focus if needed, but the cane itself is a sword-cane. A quick twist and suddenly the frail caster has himself a sharp blade on hand. Due to his lacking physical strength, however, he also tends to prefer precision strikes with the sword in order to defeat his foes.
(... It's a fun little tidbit to note that Gogon's "staff/swordcane" idea was in place well before RDM was even hinted at. Though I'm plenty happy to run with it, even if ICly he's doing Arcanima rather than Red Magic. My current headcanon is his Ver-spells are actually him briefly summoning his egis in "striker" mode to do the damage. Which means no Verthunder since he only has the base three.)
Judge Jredthys:
The Judge is... well, he has yet to actually fight to his full capacity. Even when called out as an opponent during the Grindstone, he refuses to use his weapon "Verdict" due to his stubborn belief that it should only be used to pass his judgements (i.e. kill people). As the Grindstone is a non-lethal event, he instead resorts to clumsily doing hand-to-hand.
That said, while he may lack the style and finesse of a trained pugilist or monk, the armored behemoth packs a staggering amount of physical power in his frame. As such, his albeit simple punches and throws have a dangerous amount of force behind them and one shouldn't underestimate the damage even a single hit can inflict on them. Couple that with his armor and tenacity, and the last thing anyone would likely want is a protracted close-range battle with him - he's likely to win the war of attrition, seeing as he only needs to land a few blows to lay his opponent low.
That said, he's not without his weaknesses. As mentioned, his pugilistic skills are horribly basic and - as such - can easily be read and avoided by the more skilled and agile fighters. His ranged ability is also quite limited, reduced to mostly either trying to close the gap or using his prodigious strength to throw something at the target. Add to all that, there is the fact that - despite his durability - an ancient injury has left him with an "Achilles' heel" at the base of his spine. Even if his opponent doesn't learn of it and strike at it directly, Judge's "bad back" has a chance of acting up and even further limiting his movements.
So, even from just a physical standpoint, Judge can be an imposing and downright dangerous opponent, but not insurmountable. And then you add in his strange aetheric ability and things get far more interesting. Dubbed his "Law Magic" for simplicity's sake, Judge can invoke and enforce "rules" upon the battlefield and its combatants. These can range from forcing certain types of fighters from entering certain areas, causing aetheric shock if an action is taken that is against the "rules," or even granting a boon to those who follow his decrees.
... He also has the ability to heal people, but it's not recommended. It is literally him aetherically commanding someone's body to recover, and there is nothing in place to soften the actions that follow. So the target will feel their flesh and muscle stretch out to rejoin and their bones shifting back into place and fusing back together. It is not a pleasant experience and, if the damage is severe enough, the shock to the target could do more harm than help. Which is probably why he just sticks to his potions at the Grindstone.
Gogonji Gegenji:
If Gogon had his way? He wouldn't fight. Not to say that he's a pacifist like his little brother, but more that he excels in the position of being a tactician. He's at his best reading enemy movements and directing his own. He's the "Tactician" character that gives units directions in Fire Emblem - directing his forces to victory while not actually taking the field himself.
Should he be forced to fight for himself, though, he has his tricks though he's not as grand a threat as he was once in the past (he was the Big Bad of a story arc, after all!). He was once a lot stronger then, utilizing experimental magitek devices to force synchronicity with soul crystals and drawing on both the knowledge and the power locked within those shiny stones to cause havoc on the battlefield. However, he had all that ripped from him, went into a coma, and he's still recovering even a good year and a half to two years later. Now he only really his his Arcanima to rely on, which - while decently formidable - is still not as great a skill set compared to artificially-gifted multi-job mastery.
Anyway, his delving into the mathemagical leans heavily on the basics and the Scholastic abilities of Nym. That, along with his analytical approach to combat, means he goes for attempting to read the opponent and developing an appropriate assault tactic. Until that point, he tends to focus on misdirection, enfeeblement, and bolstering his own defenses. Once he finds that chink in his opponent's armor, however, he will strike with surgical precision.
To aid in that, he's also been delving into the Allagan Summoning arts - albeit at a more restricted level due to its requirements. The primal essences needed to summon Egi were "stolen" from a Summoner soul crystal during his earlier escapades, but he has all but the tracest amounts of it at this point after the burnout. If he focuses, he can maintain a single egi but cannot Trance or do any of the higher level abilities. To get around this, his preferred method to use his egis is more of a fighting game striker assist angle. They manifest, attack, and then immediately dissipate - which also helps from a disorientation angle as well.
Should all that fail or he's dealing with someone with incredible aetheric resistances? He's not above the simple solutions. His cane - the need for which is purposely over-inflated to misdirect his enemies even before a fight begins - is a little bag of tricks. The grip has a gem in it that he can use as an added aetheric focus if needed, but the cane itself is a sword-cane. A quick twist and suddenly the frail caster has himself a sharp blade on hand. Due to his lacking physical strength, however, he also tends to prefer precision strikes with the sword in order to defeat his foes.
(... It's a fun little tidbit to note that Gogon's "staff/swordcane" idea was in place well before RDM was even hinted at. Though I'm plenty happy to run with it, even if ICly he's doing Arcanima rather than Red Magic. My current headcanon is his Ver-spells are actually him briefly summoning his egis in "striker" mode to do the damage. Which means no Verthunder since he only has the base three.)
Judge Jredthys:
The Judge is... well, he has yet to actually fight to his full capacity. Even when called out as an opponent during the Grindstone, he refuses to use his weapon "Verdict" due to his stubborn belief that it should only be used to pass his judgements (i.e. kill people). As the Grindstone is a non-lethal event, he instead resorts to clumsily doing hand-to-hand.
That said, while he may lack the style and finesse of a trained pugilist or monk, the armored behemoth packs a staggering amount of physical power in his frame. As such, his albeit simple punches and throws have a dangerous amount of force behind them and one shouldn't underestimate the damage even a single hit can inflict on them. Couple that with his armor and tenacity, and the last thing anyone would likely want is a protracted close-range battle with him - he's likely to win the war of attrition, seeing as he only needs to land a few blows to lay his opponent low.
That said, he's not without his weaknesses. As mentioned, his pugilistic skills are horribly basic and - as such - can easily be read and avoided by the more skilled and agile fighters. His ranged ability is also quite limited, reduced to mostly either trying to close the gap or using his prodigious strength to throw something at the target. Add to all that, there is the fact that - despite his durability - an ancient injury has left him with an "Achilles' heel" at the base of his spine. Even if his opponent doesn't learn of it and strike at it directly, Judge's "bad back" has a chance of acting up and even further limiting his movements.
So, even from just a physical standpoint, Judge can be an imposing and downright dangerous opponent, but not insurmountable. And then you add in his strange aetheric ability and things get far more interesting. Dubbed his "Law Magic" for simplicity's sake, Judge can invoke and enforce "rules" upon the battlefield and its combatants. These can range from forcing certain types of fighters from entering certain areas, causing aetheric shock if an action is taken that is against the "rules," or even granting a boon to those who follow his decrees.
... He also has the ability to heal people, but it's not recommended. It is literally him aetherically commanding someone's body to recover, and there is nothing in place to soften the actions that follow. So the target will feel their flesh and muscle stretch out to rejoin and their bones shifting back into place and fusing back together. It is not a pleasant experience and, if the damage is severe enough, the shock to the target could do more harm than help. Which is probably why he just sticks to his potions at the Grindstone.