According to Wikipedia, you have to make sure your song is a parody and not satire. A parody should poke fun at the song itself, while satire makes fun of something else with the song. In practice though, people rarely follow the definition of parody, and in the end, it all comes down to whether the company sets up a claim or not. Sometimes it ends in content ID claim (which can sometimes be successfully disputed), the removal of the video, or nothing at all. It's up to you to take the risk, but I'd say you have a good chance of not getting any negative consequences.
Wikipedia is not a good source... Here's something directly about this from my business law book:
"Copyright infringement occurs when a party copies a substantial and material part of the plaintiff’s copyrighted work without permission. The copying does not have to be either word for word or the entire work. A plaintiff can bring a civil action against the alleged infringer and, if successful, recover ( 1) the profit made by the defendant from the copyright infringement, ( 2) damages suffered by the plaintiff, ( 3) an order requiring the impoundment and destruction of the infringing works, and ( 4) an injunction preventing the defendant from infringing in the future. The court, in its discretion, can award statutory damages for willful infringement in lieu of actual damages. The federal government can bring criminal charges against a person who commits copyright infringement. Criminal copyright infringement, including infringement committed without monetary gain, is punishable by up to five years in federal prison." (Cheeseman, 2013)
"A copyright holder’s right in a work is not absolute. The law permits certain limited unauthorized use of copyrighted materials under the fair use doctrine. The following uses are protected under this doctrine: ( 1) quotation of the copy-righted work for review or criticism or in a scholarly or technical work, ( 2)
use in a parody or satire, ( 3) brief quotation in a news report, ( 4) reproduction by a teacher or student of a small part of the work to illustrate a lesson, ( 5) incidental reproduction of a work in a newsreel or broadcast of an event being reported, and ( 6) reproduction of a work in a legislative or judicial proceeding. The copyright holder cannot recover for copyright infringement where fair use is found." (Cheeseman, 2013)
Reference
Cheeseman, H. F. (2013).
Business Law: Legal Environment, Online Commerce, Business Ethics, and International Issues (8th ed.). Upper Saddle River, NJ: Prentice Hall.
