The first mention of the "Champions of Oceania" was in 1995, but little information was detailed about who or what they were.
In 2000, when the Soltan Star Empire invaded Earth, miraculously, Oceania was never invaded or attacked by the Soltans. Rumors to this day revolve around two possibilities: collusion with the Soltans or a VERY powerful 'Champion of Oceania' was used to prevent attack, deflect an attack or make Oceania invisible to the attacking aliens. to this day, only the elite of Oceania know this answer.
Other than prior classified encounters (detailed in GUARD's reports to the United Nations Security Council), the Champions of Oceania finally made its world debut with the announcement of the Champion's new leader, Doctor Goodthink. Almost immediately, three 'existing' Champions were removed from the team, never to be seen again.
Propaganda to this day only shows the Champions of Oceania is a popular, positive light: feeding the hungry, giving blankets and clothes to new citizens arriving at the docks, and, of course, footage of them fighting off 'warmongering' nationalist invaders such as the Commonwealth super group and dozens of other hero groups, all of course showing the Champions always winning in the end.
Today, the Champions of Oceania are considered the 'people's champions', participating in parades, being honored with their national "Champions of Oceania" holiday, and of course medal ceremonies and prestigious propaganda films showing the 'doubleplusgood' qualities of the Champions.
Although Doctor Goodthink is stated to be the leader, it is believed he's nothing more than a puppet for Governor Goldstein in running the team.
No base was ever made for them. With recent changes to City of Heroes: Homecoming, though, this base will be built soon (tm)!