Parody songs tend to have a short shelf life, most revolve around current events, pop culture or advertising, which is why I am including a brief explanation under each.

About the 1983 fervor over an ugly doll that you didn't "buy", you "adopted."  They were the must have toy for Christmas, and were quickly sold out.

Relatively recent history: about the BP Oil spill and their arrogance.  Animation done by Portley Colwell at Punch Films

"Cabbage Patch Fever"

"The BP Hillbilies"

"I'm a Mac"

This was based on the "I'm a PC" ad for the Vista operating system, that featured a cute little girl doing all sorts of cool things on a PC.  Vista was 2007's answer to the Vega.

"409"

Gas prices. Nuff said

"I'm Being Followed"

Cat Stevens, who changed his name to Yusuf Islam, was turned away for being on a no-fly list due to his religious conversion.  I think the TSA just hated his songs.

"Six Days on the Ike"

Anyone who has ever driven (see "sat on") the Eisenhower expressway knows this one too well.

"The Ballad of Bowling Green"

Making fun of the Kellyanne Conway fictitiious report that there had been a massacre at Bowling Green.  

"Are you Hungry Tonight?"

Making fun of Elvis

"Crossreeds"

Ok, not so much a parody as a mashup:

What would Crossroads have sounded like if Jerry Reed had been in Cream instead of Eric Clapton.

"Jussie Smollett, the Musical"

I did this when it was first news, and I'll bet it's still going on, and on. and on.......

   "Why Are You Standing There?"

Another Mashup:  What would "I Saw Her Standing There" have sounded like if Paul McCartney had been in Lynyrd Skynyrd.