Bradyon Veda is one of the hardest to read VNs out there... right up there with Kajiri Kamui Kagura, if for different reasons.  One reason is the frequent usage of internal jargon, obscure (to an outsider) physics terms, and other setting issues.  The other reason is that the writer is, similarly to Masada, in love with spellchants and rarely-used kanji.  That said, Bradyon Veda is science fiction and science-fantasy, not fantasy. 

One of the biggest distinctions between this game and fantasy ones like Dies Irae is that, while some of the feats performed by the Scribes seem magical in nature, they don't have any of the vagueness you tend to see with fantasy (it's maaaagic).  For instance, Naoto, the protagonist, has two favorite techniques... one that involves making metal that he can reform at will, the other where he manifests explosive weapons of various types (such as an anti-tank projectile or a shrapnel bomb).  While the method he uses is extraordinary, what he creates is in some ways mundane.  This game doesn't leave much explained... but as a result, you usually end up either with a headache or information overload, lol.

Now, to explain the most basic elements of the setting (because the deliberate under-explaining of the writer makes the game even harder to grasp in your first path than it needs to be).  First, the Divine Particles... Shinsei Souryuushi are a type of particle that causes alterations to all other known particles it comes into contact with and isn't effected by the passage of time.  Those fighting in this game are utilizing ASCs, devices that allow humans to expend enormous amounts of raw energy to manipulate these particles in order to further manipulate the physical realm.  Those who use an ASC to fight are called Scribes.

There are two types of Scribe... a 'Normal' Scribe and an 'Another' Scribe.  Normal scribes are humans altered cybernetically or genetically to allow them to utilize an ASC effectively, turning their body into a natural conductor for Divine Particles.  This allows them to create limited effects (such as manifesting nanofibers, sound waves, plasma, etc) utilizing their brains in combination with the calculation units in the ASCs.  Another Scribes are another issue entirely.  While they seem human in appearance, Another Scribes are actually Quantum Brains implanted in a humanoid body at the cellular level.  As such, their entire body can function as a 'brain', allowing them to calculate on a level so much greater than a Normal Scribe that they are not even worth comparing.  No, this isn't a spoiler.  Naoto, the protagonist, is internally frank about what he is, but it is fairly late by the time someone explains any of this, except by implication...  Quantum Brains are the final evolutionary step of a race they refer to as the Originals, humans from another parallel universe who discovered Divine Particles at a relatively early stage and discovered how to encode personality and intelligence into Divine Particles in order to allow a human-like consciousness to travel between parallel universes (referred to as time-space fields in the game).  These Quantum Brains, when they manifest on a planet, are generally implanted into an artificial body reconstructed to imitate the genetic pattern of the originals upon arrival in a particular parallel universe, because without a humanoid body, they can't physically interact with the universe around them.

The setting for the two heroine paths (Shion and Kaede) is a Japan about one thousand years in the future, in a parallel world where everyone pretty much had no hesitation about using nukes in war, lol.  Japan, having gone insanely nationalist once again, tried to conquer Asia (again) and was defeated by an alliance of white people (again).  However, the resulting warfare was a thousand times worse, nukes reducing much of the Asian continent to a wasteland.  The game begins with Naoto and the other nine members of the Nephilim unit deserting the alliance army after one-sidedly slaughtering (really massacring) the Japanese armies in Mukden (modern Shenyang), resulting in Japan's surrender and occupation.

The reason why it is easy to be confused is that technology hasn't really proceeded much past what is possible today until relatively recently in that world's history.  The over-use of nukes and a constant cycle of endless wars kept technology and society from proceeding beyond a certain point.  The biggest differences that can be seen in the Japan of a thousand years in the future are the fact that a female Empress is accepted by Japan and nationalism wasn't abandoned after the war's loss... 

 

Naoto

Fujishiro Naoto is the protagonist of the story, a former member of the Nephilim who is seeking to exterminate his fellow Another Scribes in the belief their kind can only bring harm to the world around them.  He isn't kind-hearted by nature, but he is, in comparison to his fellow Anothers, far more empathetic toward humanity (since the others barring Shion see humans as insects or pebbles in the road).  Naoto is the only all-rounder amongst the Scribes in the game, in the sense that he can step into just about any area of expertise to an extent but can't really be said to be the master of any.  His advantage is his adaptability, more than anything.  He uses hand symbols (Naruto fans rejoice) and Buddhist sutras as codes for his techniques.   He has an inordinate fondness for sweet cocktails and old music, which is laughably absurd considering his youth and lack of a trenchcoat and hat, lol.

 

Kaede

Kaede is the first heroine... a Normal Scribe who once worked for the Japanese military but now serves as an intelligence agent/investigator for the puppet government.  She is a very straightforward character, still bound by military mores and habits even years after the war has ended and all she knew collapsed.  She falls in love with Naoto almost immediately, mostly because he is just her type, lol.  She is the daughter of a family that once served the Japanese Imperial Family directly, until they were disgraced as a result of betraying the other families to the Japanese government of the time.  As a result, she is even now driven by a need to prove her loyalty to the current Empress (a pre-pubescent girl wise beyond her age called Yomiko) through her actions in service of the Japanese people.

 

Shion

Shion is a former member of the Nephilim and currently the head of the Japanese police's Scribe unit.  Unlike Naoto, her technique tends to rely on a combination of stealth and misdirection (she can make herself truly undetectable, for one thing), though she also has some pretty bad-ass combat techniques, such as dissolving her body and reconstituting it inside an enemy's body, tearing it apart from the inside (pretty guro, lol).  She has a harsh, unforgiving personality, and she doesn't really know how to display affection properly.  Naoto is pretty much the only person she ever trusted.  Like all Another Scribes, she has a cold, rational way of looking at any situation that disregards facades others try to put up without any need for thought.  As a result, she frequently comes out seeming excessively rude, but she actually has no particular malicious intent. 

 

The story of this game is... complex.  Kaede's, Shion's, and the True path are all pretty complex with the heroine routes possessing enough content to make a VN in and of themselves.  Is it a fun ride?  Yes.  However, this game goes from obfuscation to infodumping at odd times, and I honestly think that the writer's decision to make up such an extensive amount of internal jargon was a mistake.  That said, the fights are awesome, the story for each individual path is well-written, the characters' motives are understandable and internally consistent... and it is all bound together by a writer with a strong grasp of how to switch prose styles between scene types in order to enhance the experience. 

This game also has some seriously emotional moments.. I'll be blunt, don't look for a good ending in this game.  Naoto's lot in life (no matter where and when he is) sucks dog tail, and the same can be said for the other Anothers as well (Viva in particular can't seem to get a break).  There are some seriously bad-ass fight scenes, especially toward the end of each path... and the game as a whole leaves you feeling exhausting and satisfied... if you can keep it all straight in your head in the first place.