I don’t know that I would have called it a “radio” effect. It sounds like “fuzz guitar” effect for a voice. I’d probably copy a clean (sometimes called “dry”) voice track to a second track and apply Effect > Hard Limiter or Effect > Leveler to the second track. You can make each track dominant to taste. You can apply the tricks to the first track, but that’s harder to recover from if something goes wrong.
There is an Auto Chorus affect that may be custom. I don’t see it in the regular effects list. That should give you the second part of that song.
Remembering, of course, that Audacity Projects do not save UNDO. Don’t do anything that affects original tracks.
Make a duplicate of the original voice track.
Apply one of the “Broadcast Limiters” to the track with a heavy setting so that there is a lot (too much) distortion (http://wiki.audacityteam.org/wiki/Nyquist_Effect_Plug-ins#Broadcast_Limiter_II)
Apply the High Pass filter - frequency about 1000 Hz, roll-off 12 dB per octave.
Amplify so that the peak level is 0 dB.
Adjust the levels of the original (unprocessed) track and the new (processed) track to give the desired amount of effect.
Select the two tracks, then use “Tracks > Mix and Render” to mix these tracks into one.