What radio signal have NASA transmitted to outside our solar system and what did they contain?
Every command sent to a satellite or space probe from Earth continues traveling, forever.
At some point it becomes so weak it's impossible to interpret, of course, but NASA routinely receives data transmitted from the two Voyager spacecraft, both of which are now on the outer side of the Solar System's boundary shock, and both of which, due to aging of their onboard power sources, now transmit at only a few watts (directional transmission helps a lot, but even so, large dish antennas are required on the ground).
Similar equipment to the large dishes at Very Large Array, Green Bank, etc. could receive commands intended for, say, a Mars orbiter to distances well beyond the heliopause.
There have been intentional transmissions toward other star systems, as well (at least one globular cluster was targeted by a strong transmission from Arecibo, though that signal will not arrive for another few thousand years), but none were initiated by NASA. NASA, as far as I know, adheres to the United Nations protocol prohibiting attempting contact with extraterrestrials without the consent and supervision of the United Nations.