Well, there is "satire," which has acquired the meaning of a caricature or burlesque aimed at something other than the original work. That is, your song, which takes aim at "big corporations ripping off the public," is a satire, not a parody. In fact, there is a distinction between these two words in copyright law, in that parodies are "allowed," but a satire using copyrighted material (tune or lyrics) is not "allowed." I put the quote marks around "allowed" because of all the wiggle room that court decisions and general practice have given this. A recent court case involving "Pretty Woman" is an example -- that "song" (to give the benefit of the doubt to the defendant's "work") was a parody, making fun of the original song (think Homer and Jethro, but more tasteless). "Charlie on the MTA" is a satire, BTW, since it was a political song using an old popular song (19th C) as its starting point.

So I'd just use "satire" for songs which fit the definition you give.

And it's "Deck Us All with Boston Charlie," not "Deck the Halls ..."

Bob Clayton