Is it possible for a person to fly with mechanical wings attached to his torso?
You could reasonably call a hang glider "wings strapped to the torso" for this purpose -- hence the answer is "yes, sort of."  With a well designed glider, one can launch from sloping ground and soar on slope lift or thermals, limited by oxygen requirements and fatigue.  Hang gliders have done cross country flights running to many hours, stayed up literally dawn to dusk on ridge lift, and flown high enough for the pilot to require oxygen (and then some, I believe the altitude record is around 18,000 feet).

None of this, of course, is powered by the pilot, using either arms or legs, but this is clearly "wings strapped to the torso."

Add a small engine and you get a modern ultralight/microlight, or something like Rocketman's jet powered wings.  The latter, especially, is still pretty clearly "wings strapped to the torso."