I have to ask… when was this from?? I don’t remember it at all, and there’s something comically brilliant about the way it all fits!! 
I heard it first at DisneyWorld at the Adventurer’s Club as;
Dough; the stuff I buy beer with…
Ray; the guy I beer from…
Me; the guy I buy beer for…
Fa; the distance to the store…
So; I think I’ll have a beer…
La; lalalalalala…
Tea? No thanks I’ll have a beer…
Which brings us back to Dough…
And the fact that it’s Tony Bennet makes it all the greater.
Sung by Lisa in the episode when the power plant employees go on strike:
*Gather 'round children, it’s high time you learned
About a hero named Homer and a devil named Burns
We’ll march day and night, the girls and the fellas
We’ll fight to the death or else fold like umbrellas
So we’ll march day and night by the big cooling tower
They have the plant, but we have the power*
When Lenny has her play Classical Gas, it’s just icing on the sake
This seems to have circulated around the Internet. It never appeared in a Simpsons episode.
Besides, everyone who watches The Simpsons knows that Homer buys his beer from Moe, not Ray.
It was a parody of Talkin’ Baseball (Willie, Mickey, and the Duke), and was written and performed by that song’s writer/singer, Terry Cashman. But I don’t think the original has anything about humorous tragic illnesses or grotesquely swollen jaws (two lines I love).
Disco Duck and Fleetwood Mac
Playing on our old 8 track
Michael Jackson still was black
Those were the days!
In “Dumbbell Indemnity” as Homer commits car theft so Moe can file an insurance claim:
Stealing, stealing, stealing a car for Moe
Da da, da da, da da, da da, insurance fraud today
(To the tune of ‘Sailing, Sailing’)
I can’t believe this thread has already almost been a page long and there’s been no mention of the classic ad jingle…
Call Mister Plow
That’s the name.
That name again
Is Mister Plow.
[sub]Written by Jeff Martin, ©1992 TCF Music Corp. Used without permission[/sub]
I like all the songs in the Streetcar episode.
I always crack up in the episode featuring Malibu Stacey - The Musical featuring Mr Smithers singing:
Sold… separately… Sometimes I feel like I’ve been sold… separately…"
You are correct, there was however a clip I saw that was made recently with those lyrics with homer in the bar shown in a special or an outtake (what would the creators of those lyrics do? Sue Homer’s creator after they implied Homer made them? 
The Simpsons creators are famous for paying attention to the Internet.
Ditto:
*New Orleans
Tacky, overpriced souvenir stores
New Orleans
Home to pirates, drunks and whores
If you wanna go to hell
You should take a trip
To the Soddom and Gommorah on the Mississipp*
and
A stranger’s just a friend you haven’t met
You haven’t met
Streetcar!
Even better was Bart’s apology on the chalkboard the following week:
“I will not defame New Orleans”
Do you have a cite for that?
*Luke be a Jedi tonight. . .
Luke be a Jedi tonight. . .
*
We are the mediocre Presidents
You won’t find our faces on dollars or on cents
There’s Taylor! There’s Tyler! There’s Fillmore and there’s Hayes!
There’s William Henry Harrison, “I died in thirty days!”
Who needs the Quik-E-Mart? I doooooooooooo…
Hey, he lied to us through song! I hate it when people do that!
Flanders tries to wreck my song
His views on birth control are wrong
and later
If you dislike polite left-handers
then I doubt you’d like Ned Flanders
I’m walkin’ down the street
and I’m singin’ what I’m thinkin’
Hey look at that dog!