[quote=IncredibleBee]
It's probably an international organization created under the UN with leaders, crew, and funding coming in from the US, Japan, England, China... basically any major nation.With that in mind, we likely answer directly to the organization's director. But the director answers directly to the world's leaders. We'd actually probably be kept under super close watch specifically to avoid agents going rogue.
[/quote]

I figured a team like this, filled with so many strange factors, would have to be some high ranking Earth Gov commanders baby. Sort of like the Avengers. Like there's one person or a handful of people really pushing the idea that what Earth needs is a dedicated task force for when things get real. Not "this country has declared war on this one" real or "terrorists have taken a cruise ship hostage" real, bigger than that. 

"We don't know what it is, but it crawled out of the ocean and smashed Tokyo."
"Terrorists have taken the president, his family, and new super prototype we were demonstrating."
"They're going to take the colony and [i]drop it![/i]"

Those sorts of problems. And I imagine we have a ship or something that ferries us around to deployments, like the Tuatha Dé Danann.