Can Audacity do this..?

Hello, I'd like to ask if Audacity or any other free [quality] audio editors can do this kind of filter on the music::

Please listen all the samples (since I'm might mistaken them for something else)::

http://www.youtube.com/watch?v=AC6REhy5L38

(Good example here, from 0:30 - 1:04.. the same thing is throughout the whole song)

http://www.youtube.com/watch?v=9Gc75dMUGX4

(The first like, 3 seconds. It's the first line that the she sings)

http://www.youtube.com/watch?v=mGDxk4dE_CU

(First 25 seconds.. I'm not sure if this is the same effect, but it might be)

The kind of thing I'm asking is what makes that headphone-ish effect? What is its name?

If the effect can't be done in Audacity, what other audio editor can? Preferably, I'd like it to be free or have a trial/demo version, and enables you to record from a microphone.

Thanks!