Japanese Wikipedia has been nice enough to give summaries of the kaiju's roles, so here's what happens to each of them to the best of my ability to translate:
Kamacuras: The first Kamacuras was killed by bunker buster bombs after attacking New York in 1999. By the 2030's numerous Kamacuras inhabited the U.S., along with Kumonga.
Dogora: Killed by spider venom being released from chemical plants in the UK and Europe in 2002 after it attacked London.
Kamoebas: At least four individuals appeared. The fourth Kamoebas washed ashore dead on Odo Island in 2030, and was the first evidence of the existence of Godzilla.
Rodan: The first Rodan attacked Beijing with the first Anguirus in 2005, but they were both killed by Hedorah. However, sometime later flocks of Rodan were present in Siberia and preyed upon refugees fleeing Europe.
Anguirus: The first Anguirus was killed by Hedorah along with Rodan in 2005. A second Anguirus attacked South Africa a year later, but its fate is unknown. A fourth Anguirus was killed by Godzilla in Los Angeles in 2030, along with Varan II and Baragon II.
Hedorah: Hedorah was a bioweapon created by the Chinese, but went out of control after it killed Rodan and Anguirus. It destroyed Beijing and Tianjin, then vanished after it consumed all pollutants in the area. It's safe to say Hedorah's fate is unknown.
Gabara: I had a difficult time translating this, but it sounds like Gabara was injured in an explosion and fell into a river and was eaten alive by crocodiles and piranhas. Gabara was only about 10 meters tall, so he was smaller than many of the other kaiju.
Dagahra: Dagahra attacked Australia in 2017, and was eventually fatally wounded by the Australian military and flew out to sea and died. However upon death he released a ton of Barems into Australian waters, which arguably caused more devastation than him.
Orga: Orga attacked Turkey in 2022. No details are given about his defeat, but it gives the impression that he was stopped.
Megalon: Megalon appeared in 2012 and destroyed several countries along the west coast of Africa. He returned in 2022 and completely destroyed South Africa. No details on his fate.
Griffon: Appeared in Cairo in 2021. They were seemingly defeated before they could reproduce and spread. Japanese Wikipedia says that this Griffon is meant to be the individual from Latitude Zero, which is consistent with the Japanese spelling of its name.
Gezora: Terrorized the Mediterranean in the late 2010's, hindering refugee movement out of Europe. Fate unknown.
Giant Octopus: Lived in the Pacific Ocean, and sank several fishing boats and transport vessels every year. Fate unknown.
Ganimes: Attacked American crab fishing boats in the Bering Sea. Fate unknown.
Manda: First appeared in the Atlantic in 2022 and terrorized it for years. He was finally destroyed by the Gotengo in the Strait of Dover 2039 as part of "Operation: Eternal Light," a mission to regain control of the Atlantic Ocean from the kaiju.
Varan: Multiple individuals appeared, but the second Varan was killed by Godzilla in Los Angeles in 2030.
Baragon: Same case as Varan. Multiple individuals appeared, but Baragon II was killed by Godzilla in LA in 2030.
Maguma: Destroyed North Korea in 2024 then moved into South Korea. Once Maguma approached Seoul, the U.S. launched a tactical nuke and killed him.
Kumonga: Lived alongside Kamacuras in the U.S. in the 2030's. No details on its fate or how many there were.
Megaguirus: No details yet.
Biollante: Appeared off the coast of Normandy in 2039 as "Operation: Eternal Light" was underway and took G-Force by surprise. She was defeated by Moguera when it burrowed into her roots and destroyed her "heart."
Zilla: When the first Zilla was killed it was misidentified by the French as Godzilla because it also was a bipedal creature with back fins and a long tail. Unfortunately Zilla was capable of asexual reproduction and quickly overran France, and frequently preyed upon refugees fleeing from Godzilla himself. Zilla was eventually wiped out by G-Force, but at great cost and difficulty.
Gorosaurus: Appeared in Paris after Godzilla destroyed it. Gorosaurus was killed by the combined efforts of G-Force and the Bilsards in 2039.
That's all I have so far. Keep in mind the translations are rough at best, and I'm sure some details aren't entirely accurate. Some of these details have been explored in greater depth already, and I'm sure others will do a better job than me at documenting all of this later.