Note: I would have to be very advanced in Japanese or have a Japanese friend explain to me in order to convey the finer points of the plot, but I'll do what I can...

This movie is NOT a sequel to Godzilla 2000. It is, in fact, the beginning of another timeline, so there is no way in hell I can tie it into the others. 
We delve into the past, in 1954 during Godzilla's first attack on Tokyo (the scenes were actually recreated using the Godzilla2000 suit!) There is no Oxygen Destroyer, Godzilla simply disappears back into the ocean. 
Then we cut to a flashback of Godziilla attacking a power plant in 1966. This attack leads the government to ban nuclear energy and switch to plasma energy.
In 1996 the beast attacks again and a military woman named Tsujimori is running with the rest of her platoon. Ducking between buildings, the soldiers take turns firing at Godzilla with their bazookas. Things go terribly wrong when Godzilla grows even more violent and angry than ever and hunts down the platoon. It knocks down a building structure. Tsujimori's commanding officer pushes her out of the way a millisecond before the falling rubble crushes the life from him.
Tsujimori, unhurt, rose from the ground. She sees her officer's feet sticking out of the ruins. Disbelief and shock gives way to molten rage as she picks up her bazooka. Letting fly a terrible scream of anger and grief, she pulls the trigger... 

and we then see the title, "Godzilla Vs. Megagiras" in Japanese.

Five years later, a new weapon has been developed called the Dimension Tide. From an orbiting satellite, a "black hole" missile is fired, sucking its target into another dimension. (What it really does is create time rips through which objects can pass! Hence, the presence of the prehistoric insects called Meganurons!)
It is developed mainly as an anti-Godzilla weapon. Understanding their own inability to kill Godzilla, someone comes up with a brilliant plan to stop him. 
The first test of this new weapon on a house somewhere in the desolate countryside results in a breach of this dimension by Meganurons, a huge hungry dragonfly... hungry for blood and very carnivorous. Some dumb kid finds an egg and brings it home for a pet, then, deciding that the egg's constant output of water unnerves him, drops it into the Tokyo sewer. Unfortunately for Tokyo, it  ends up under water and infested with Meganurons.
The war against Godzilla is on as bravehearted Tsujimori singlehandedly takes on the beast and manages to attach a tracking device on his thick hide before he disappears into the ocean. The military keeps track of both monsters. 
Godzilla battles a swarm of Meganurons (which could very easily have been filmed the cheap, easy and realistic way, by buying a first class round trip ticket to Syracuse, driving all the way up to Oswego, and setting up a camera on Will Dowie's front porch... these people have mosquitoes that are the size of F-14's!) He torches them as the black hole missile hits....

...blowing everything away in its path.

...except for a familiar row of jagged spines, which pop up to reveal the Big Guy, still here! And he does open a can of whupass. Godzilla destroys Megagiras after a long, protracted battle with much bodily violence, only after catching the latter's stinger in his mouth. Then he goes berserk and begins to trash the place.
A plan is devised to activate the Black Hole missile at the cost of the satellite and the Gryphon (Tsujimori's flying battle cruiser). Godzilla sees the swirling vortex open up above his head and fires his atomic ray into it, to no avail... he is sucked inside. Everybody's happy, everything is groovy, Tsujimori lets down her hair, and life returns to normal... but not for long....

*credits roll*....

We see the kid who dropped the egg down the sewer cleaning up after class, minding his own business until a commotion ensues and he hears a familiar roar... Godzilla is back and someone's got to pay!

My thoughts on this film:

This film came with my boyfriend's projector, and I had been waiting anxiously to see this film for a year and a half now. What made me mad is that I was so tired, I fell asleep halfway through. :)
When I got to see the rest of the movie I was, to say the least, very impressed. Though my comprehension of spoken Japanese is limited, I could sort of make out the plot line. The monster scenes from 1954 were definitely cool although I personally thought a Y2K suit and CGI special effects looked kind of out of place in a 1954 setting. The omission of the Oxygen Destroyer from the plot line sets a new story line in which this indeed is the original Godzilla. In other words, the agonizing death of the first Godzilla, and the other movies never happened... a rather infuriating, if consistant, trend on Toho's part. But it is convenient to setting the tone of the story.
I would rate Godzilla Vs. Megaguiras as a science fiction fantasy with elements of "Mosquito" and "Ultraman" thrown in for good measure. The Megagiras and Meganurons are beautifully executed through CGI effects and are effectively brought to fruition as nasty, vicious, murderous creatures with insatiable bloodlust go, as we see when a smoker and his unfortunate girlfriend are hacked to pieces in a gruesome manner. To be sure, this is a dark, intense film with a pulse pounding score (and the new composer, who happens to be a woman, did a tremendous job!!!!) although there are a few silly moments. I don't know which is more deserving of 40 wet lashes with a ramen noodle, Godzilla flying through the air, or getting up after eating floor and shaking his head like a dog getting water out of his ears. But, despite the silly moments and the generally far-fetched plot, this is one of the best films I've seen yet and the ending was intense!!! You don't actually see the return of Godzilla, but the look on the little boys face says it all!

BACK

Premise (quoted from official site): "Ever since its first attack in Tokyo , monster king Godzilla has destroyed Japanese cities that lay in its path in search for energies that fill its appetite. Soon, it became Japan's top national priority to develop a source of 'clean energy' that would not stir up Godzilla's appetite. In 1996, the Clean Energy Factory led by Motohiko Sugiura (Ibu) developed a new plasma power generator in metropolis Osaka. The success seemed guaranteed - but, not for long. Godzilla appeared again, and demolished the entire power plant. Members of a special combat unit risked their lives in this doomed fight. One of the members, Kiriko Tsujimori (Tanaka) tried to load shell in the rocket launcher. But while she was desperately trying to stop her hands from shaking, her much respected commander - Takuya Miyagawa (Nagashima) lost his life under the falling concrete debris of the power plant." 

"Now, in the year 2001, Kiriko leads the 'G-Graspers' - a special anti Godzilla unit in the 'G-Command', which is a new division created in the Ministry of Defense after the destruction of metropolice Osaka. Her sole purpose of life now is to exterminate Godzilla. She has powerful support from a physicist Yoshino Yoshizawa (Hoshi). The plan is to wipe out Godzilla completely as simply killing it merely creates hazardous radiation leakage. The best solution, therefore, is to create an artificial 'black hole' which will suck in everything into another universe. The difficulty is to reduce the size of the weapon to 2 meters in diameter - a size small enough to be carried on a satellite. A young inventor has the answer. Hajime Kudo's (Tanihara) long and hard working days produce the ultimate weapon: the Dimension Tide." 

"Tests continue on the operation of the man-made black hole. One day, Yoshizawa and the team accidentally causes the black hole to create a distortion in the time dimension. An uninvited intruder comes through this hole. An ancient giant larval 'Meganulon' finds a new home in modern Japan. Meganulons need water to grow. So they find water veins under the city of Shibuya. They break the water veins, flood the city and use this newly formed lake in Shibuya to multiply and grow. As the swarm grows, humans become their favorite targets. But this was only the beginning. As the Meganulons metamophose into adult Meganulas, they get attracted to Godzilla's enormous power. They attack Godzilla to suck in its energy and inject it into their special larva that would become a gigantic dragonfly - a 60 meter long Megaguirus!! It is now Megaguirus's turn to attack Godzilla to devour its energy." 

"A three-way battle between Godzilla, Megaguirus and humans! The battle for survival in Odaiba! Can humans really exterminate Godzilla? And... is there a future for Japan!?"