Apparently, you hadn’t heard.
Yes has tons of weird lyics, but this one I heard about.
"* Yes lead singer Jon Anderson and guitarist Steve Howe wrote this song near the end of a tour when they were traveling in Scotland. They were in the back of a van going from Aberdeen to Glasgow when the song came together. Awed by the scenery, Anderson came up with lyrics like “Mountains come out of the sky and they stand there,” as the mountains would disappear into the clouds.
The band had been touring for about a month, and Anderson was looking forward to his imminent return to London, where he could once again see his wife at the time, Jennifer. The lyrics, “Twenty four before my love you’ll see I’ll be there with you” indicate that he is just 24 hours away from being with her again. He says “Roundabout” is a “happy song” and describes it as a “Scottish jig.”
- The lyrics describe a psychedelic-country life, with allusions to driving. A roundabout is a kind of traffic circle that substitutes for a stoplight and confounds tourists who are unfamiliar with them. Traffic patterns don’t always make the most poetic lyrics, but the word “Roundabout” sings very well and fits with the theme of the song, as when Jon Anderson came to a roundabout in Scotland, he knew that he was almost home."
Still haven’t, but looking around at other interpretations, some are that it’s a stream-of-consciousness about the banality of life; another long take on it was that it’s about tabloid journalism and that the chorus refers to the practice of selling organs for money. That’s the fun of songs like these – they’re just completely open to interpretation. Looking at it again, it does paint a fragmented, disjointed picture and isn’t totally random words picked out of a dictionary. (And the words picked are picked for their punch.) So perhaps it’s not quite a caricature of the banality of pop music lyrics, but I think there is an aspect of that in the way it is structured as seemingly unrelated words juxtaposed next to each other. Multifaceted meanings or just plain nonsense? You decide. It’s a great song nevertheless.
A classic. That has to be linked to to those who haven’t seen it. Essentially, it’s how American or English popular music sounds to Italian ears:
Word salad inspired by Alice in Wonderland:
Let’s not forget Lucy!
Lordy, how did I forget about that one? I love that song, even if it’s nearly impossible to sing along with. 
I immediately thought of America, but all of their songs fail the “You Love” test of the OP. It didn’t ask about “nonsense songs you hate!”
Fish heads, fish heads
Roly poly fish heads
Fish heads, fish heads
Eat them up, yum!
Yes, I was raised on MTV.
“Judy in Disguise”
Alice by Pogo
Honestly this song wouldn’t be half as good without the video.
Lucy in the sky with diamonds males more sense if you know that it was supposed to be a musical representation of an LSD trip. John Fred then tweaked the lyrics, which sound weird if you don’t know the origin of his version.
Walt Kelly’s Deck Us All With Boston Charlie must be mentioned.
Yep. It was on AM pop/rock radio in the early sixties.
It was in fairly regular rotation on the oldies station that I listened to in the late 80s and early 90s as well. The Trashmen!
And of course there was the Ramones cover from Rocket To Russia.
Here’s a peppy jazzy number that’s fun to listen to. But I defy anyone here to listen and tell us what the words are: Mumbles by Clark Terry:
Sound familiar? This number was used regularly on the Soupy Sales Show, sung by Pookie the Lion. No matter how dumb you might think the Soupy Sales Show was, Pookie was always fun to watch:
One of my favourite bands is pretty much undecifer-able.
The Cocteau Twins, I mean just take one at random.
“Frou Frou Foxes in Midsummer Fires” - great song, steaming pile of nonsense lyrics. You can’t understand the lyrics as sung and even having them written down doesn’t help that much e.g.
Their fan I tickle
From serpents to dragons
I’d immerse you in flame
Your milk and your passion
Lead weight for his from his old turn
The young, I was eagerest
I’m losing the stars
I enlisted to find you
I buckle and rosed
As god and the rest(wrist)
How mere riches be
A war all we lose
Close into symbols
A fly drinks the ignitions
They turn infant’s breath my
Milk and wrap to her baby
Not that it matters, still love 'em.
Dylan’s ‘Subterranean Homesick Blues’
Simon & Garfunkel’s ‘America’
AIUI both have significant autobiographical content.
Doesn’t this disqualify them as ‘Nonsense’?
OP nailed it with much Beck and some R.E.M.
Let’s not forget Captain Beefheart. Each song has a discernible theme, but the words are often Dadaist poetry bordering on nonsense. Maybe start with “Steal Softly through Snow.”
Another, just-pick-any-song band that qualifies is The Pixies.