Yes, the TSA is part of the Executive Branch, so it ultimately reports to Obama.
On a related note, you may wish to read Friedrich von Hayek's book, published in 1944, The Road To Serfdom. He covers many subjects in this book, but one of them is the danger that arises when the legislative branch delegates wholesale powers to the executive branch, or, as you say, "has congressional oversight, but its actions are not laws. So who do we complain to?" Hayek worried about this separation of responsibility from power.
http://en.wikipedia.org/wiki/The_Road_to_Serfdom
Hayek was, in part, looking at the British system, which is Parliamentary. They have some advantage there in that there is a clear separation between the head of state and the head of government. The USA is the only democracy that has ever tried to combine these two offices. The fact that no other country has ever imitated this aspect of American government (whereas most other aspects of the American Constitution have been imitated) says a lot about what a bad idea this is. In most democracies, the people are free to show their respect and veneration for the (usually powerless) head of state, and the people feel free to show scathing disrespect to the (powerful) head of government. In the USA, the people often have mixed emotions - when you criticize the head of government, you are also criticizing the head of state, so people typically pull their punches, and use language that is more respectful that what typically gets directed at a head of government in other democracies.