In the movie The Avengers/Avengers Assemble, Loki says:
......what have I to fear?
Tony tells Loki:
The Avengers. That's what we call ourselves. Earth's mightiest heroes.....
Then why does Thor form a part of the Avengers?
He is not from the Earth. He is from Asgard.
Thor is an Avenger for a multitude of reasons.
It's worth noting that the entire plot of The Avengers/Avengers Assemble is set into motion by Thor's actions in Thor. If Thor hadn't waged a war upon the Ice Giants out of pride and anger, then he never would have been banished to Earth, and Loki would have never sent the Destroyer there to kill him. Despite the fact that Thor saved the people of the small New Mexico town, they never would have been in danger if he hadn't been there, and he holds himself responsible for that.
Fast forward a year or so, and Loki is attacking the Earth with an army of Chitauri, and Thor heads to Earth in order to stop it. While confronting Loki in The Avengers/Avengers Assemble, he specifically claims that Loki is
Attacking the world I love for recompense for your imagined slights
believing that Loki's attack on Earth is a result of a personal vendetta Loki holds for Thor, and at the same time claims that
This planet is under my protection.
On top of that, he later learns that SHIELD are creating weapons of mass destruction after learning that there are other worlds out there. Nick Fury personally points his finger at Thor as the reason they are doing so, and Thor realises that, again, his interference with another planet has put its inhabitants at risk.
After saving New York, Nick Fury knows that his plan to create a response team, known as The Avengers Initiative, has been a success. Maria Hill queries how they can protect the Earth when they have all gone their separate ways (some of them pretty far), to which Nick Fury replies;
Because we'll need them to.
Nick Fury clearly believes that the next time the Earth is in danger, the team will reform to keep it safe.
At the end of the day, Thor's initial adventures on Earth, his love for Jane Foster, his responsibility in the Destroyer's attack on the New Mexico town, and the Chitauri Invasion of Earth have all meant that Thor has an interest in (or, as he may see it, a responsibility for) protecting the Earth. By the end of Thor: The Dark World, it would seem that Thor plans on spending more time on Earth with Jane Foster — which means that Thor truly is one of Earth's Mightiest Heroes.
It's also worth noting that the initial comic book line up of The Avengers included Thor, who lived on Earth at the time under the alias of Donald Blake. The tagline for The Avengers comics was "Earth's Mightiest Heroes", and Tony's line is a reference to this.
The question is not where Thor is from, but for whom he is fighting. The Avengers fight to protect Earth. Thor may have a special interest in protecting the world because of his girlfriend, but he already tried to protect humans in his own movie, when Loki sent the Destroyer.
Also, i think Tony Stark tried to sound cool, and "Earths mightiest heroes" sounds better than "a bunch of people, and your brother is with us too, even though nobody knows why"
The above answers hit all the main points, but one more thing to remember:
The Avengers Initiative, as conceived by Nick Fury, seemed to include Iron Man and Captain America, along with some SHIELD personnel like Black Widow and Hawkeye. Bruce Banner was only invited for his familiarity with Gamma rays, and Thor was neither invited nor welcome.
But when Loki showed up, Thor wasn't far behind. Even then, when he first appeared, they straight-up attacked him. Iron Man had been briefed on him (we see Thor's file among the rest during Coulson's visit to Stark Tower), but he clearly considered him untrustworthy at best, outright hostile at worst. Without any attempt at discussion, Iron Man went into attack mode and Captain America wasn't far behind, hesitating only out of a general desire to avoid extra conflict. Cap even insists that Thor "prove it" when Thor claims to be there to stop his brother.
It was only when Thor willingly stood down and joined them on the Helicarrier that they began to trust him. No doubt Jane Foster (who they were in contact with, as Coulson mentions they moved her to keep her safe) vouched that Thor would never work with Loki against Earth, and Dr Selvig probably had some good things to say about Thor before Loki turned him. So they had some reason to trust him, and once he started playing nice, they let him in because they could use his help.
But let's not pretend that as soon as Earth was in danger, they called Thor. They didn't want him there, no doubt because they couldn't get in touch with him, but also probably for the very reasons you mentioned.
One thing I didn't see in the above answers...
Although Thor is from Asgard, he is obviously well known on Earth. In fact, he has been known on Earth for centuries!
In the Avenger's movie universe as in our own, the Norse religion holds Thor to be one of their central figures. (As mentioned in the movie, Thor) In fact, for all we know, he might've spent more time on Earth cumulatively than Tony Stark or the other humans, given he's effectively immortal. Scifi SE: How old is Thor
As major figure in Earth's history, it would seem to be perfectly reasonable to include him in its defense.
