There are plenty of songs that are definitely joke songs. Nearly everything by Weird Al Yankovic, Ray Stevens and Jim Stafford, for instance.
But while Kung Fu Fighting is silly, I don’t think it was meant to be a joke. I know Melanie intended Brand New Key was meant to be serious, but it comes off as silly.
Let’s add Midnight at the Oasis.
Any more?
Gimmee Dat Ding
Muskrat Love.
I don’t like Spiders and Snakes.
I’m sure it’s a serious sentiment.
Drop Kick me Jesus through the goalposts of Life.
Baby Don’t Get Hooked on Me
I Am I Said
We Are Never Getting Back Together
The oeuvre of Ice J J Fish continues to be hotly debated as to the artist’s degree of self-awareness. He is truly our generation’s Florence Foster Jenkins.
MacArthur Park’s metaphor about a cake left out in the rain is fairly silly.
A lot of Tom Lehrer’s songs are funny and yet serious, like “Wernher von Braun”.
C’mon, man. He’ll never have that recipe again! Have some sympathy.
Seriously, though, the fact that that song is so melodramatic and over the top is why I legitimately enjoy it. Jimmy Webb, the original songwriter, did a live performance with Paul Schaffer’s band on one of Letterman’s final shows that was simply great.
Possibly I Love L.A. by Randy Newman. Some of Newman’s songs from that era were clearly sarcastic to begin with. There’s a line in it about “look at that bum over there, he’s down on his knees”. When Newman sings “look at that mountain” the video shows the Matterhorn ride at Disneyland.
I don’t know if Newman has ever spoken on the subject, but I kinda feel like I Love L.A. is his paean to Los Angeles, warts and all. To Angelenos, it seems to be a party song, and they don’t notice the warts.
On the same note, “Short People” is another good example of the OP’s request; a serious song that sounds silly, because Newman is trying to point out how ridiculous racism and bigotry are by making up nonsensical stereotypes about a completely inoffensive group, but it just sounds like he’s really pissed off about short people for no good reason and that’s funny.
I hate that song 
Inca Roads, by Frank Zappa?
Like a lot of Phish songs, it’s very sophisticated musically, but the lyrics are goofy.
It’s not a metaphor. It’s a real cake that really got left out in the rain. I learned this while listening to Gilbert Gottfried interview Webb on Gil’s “Amazing Podcast.” This link should take you to the correct episode
That seems to happen to a lot of songs, because the hook brings you back.
Just read the wiki and Newman is quoted as saying the lyrics are ‘unambiguous,’ lol. Also, TIL that Christine McVie and LIndsey Buckingham sing/shout the ‘we love it’ parts.
Who said that? Oh, sorry, dint see you down there. 
One of those guys just seemed to enjoy writing silly love songs.
What’s wrong with that? I need to know.