The radius is quite far, my politician family is long gone, so I have created a new test family. I created 1 speaker politician (Blonde in purple), 1 listener YA (dressed in black), the politician will be giving speech to this guy. 2 teen bystanders, 1 female and 1 male. I have them stand as far as possible. I then have them move closer to the politician after each speech, until both of them can hear the speech.
Result is as follows:
Depends on how you count it, the radius is around 13~15 squares. The sim being spoken to gains relationship boost twice, once for listening, and then from the relationship boost that affects all sim in the radius.
A powerful thing about Give Inspirational Speech is, it is not limited by room. Sims not in the same room can still hear it.
Yet another powerful feature of the speech? All who listens to the speech gains relationship with each other, as if they are having a group conversation. They have never spoken to each other yet they gain relationship boost with each other.
The speech lingers for a few seconds, so if a sim stands outside of the radius, and moves within radius after the speech ends, they still gain the relationship boost.
The politician sim made 9 friends just for standing there and talking to 1 person. In conclusion, it is a really nice interaction to have. If you talk in a party, I am quite sure most, if not all sims, can hear the speech.