The US didn't invade anyone, well not recently anyways. If you're referring to what's going on right now.
To invade is to conquer or pillage, and neither of which are happening. Oh, there's warring and destruction going on but it's not actually an invasion in the defintion sense.
Don't forget that there are other nations involved as well who are fighting on the side of the US, it's not just the US.
Those other nations had a choice and they made theirs, they didn't have to follow (except those countries who are binded by an alliance treaty, but those have been broken). They could've pulled out whenever they want to instead of just sending more people over.
As for WW III, please, what's going on right now isn't even close to a WW III.
In the scope of things it's not even that big of a war, technically the US...let me rephrase that, the PRESIDENT didn't "declare" war on any country, he delcared war on "terrorism".
WW I and WW II consisted of several nations and their allies, it started with one tiny incident and blew in to a full out war, that brought in pretty much all the world's super powers. That's why it's considered a World War, and that's why what's going on isn't a World War.