Rock and roll might be the best genre of music because of everything it can incorporate. Country music is naturally sonically limited (too loud and it becomes rock). Jazz might bring the most originality, but lyrically it shouldn't stray too far into oddness.
Of course, simply being strange for no reason can come across as too planned and the track loses its authenticity. A great weird song needs to sound as if it happened almost by accident. The records the song and thinks, "Wow, we shouldn't use that but there is no way we cannot."
The four gems that follow mostly won't be heard on the radio. If they are, you should send a "thank you" note to the deejay. The disc jockey also likely has the same taste as you so that is a radio/streaming station worth saving.
Four strange songs that are worth listening to again and again
Queen - "Seaside Rendezvous" (1975)
This song is a tribute to the 1920s and fits perfectly off the band's album, A Night at the Opera. Simply paying homage to a decade that happened well before the birth of rock and roll is one thing, but Queen includes a fuzzy guitar solo and Freddie Mercury being at his Freddie Mercury-ist. In the hands of any other group, the song is silly. With Queen it all makes sense.
The band certainly did not mind taking some chances. This track was never meant to be a huge hit, but it was something the band wanted to make for themselves. That was part of what made Queen so entertaining; they just wanted the listener to have a bit of fun.
Stone Temple Pilots - "Wet My Bed" (1992)
One of the wonders about this song was how the band ever had it included on their debut album. Usually, first records belong as much to the record company as to the band because the record execs want the first album to pop in case they don't feel like keeping the musical artist around. Perhaps what makes the track seem even stranger is that it follows the slow-tempo "Plush" on the tracklisting for the LP and one might have anticipated something heavier to follow.
Instead, "Wet My Bed" sounds as if vocalist Scott Weiland just woke up, suddenly started talking to everyone else in the house, and recorded what he was saying all while the music was being recorded at the bottom of a pool. This tune was not radio-friendly in the slightest, but you will remember it for decades and never truly know why.
White Stripes - "Little Acorns" (2003)
The song is four minutes long but the first minute is news journalist Mort Crim reading about a lady who has had money problems and found inspiration to escape her concerns by watching a squirrel store acorns for winter. This leads to a song about the same. In fact, while Jack White and Meg White were recording the album in the studio they found old tapes of Crim and decided to make the song based on something Crim had read. Even Crim was initially confused.
Taken plainly, the track is simply advice not to overspend but also includes the lines, "Cut up your hair, straighten your curls/Well, your problems lie in your curls"...whatever that means. The great part is that after Crim's part and despite the simple lyrics, Jack White creates a heavy rock song that will get you off your booty.
Tom Waits - "The Black Rider" (1993)
This is likely the best "strange" song ever made. The track is certainly not rock, but it isn't exactly anything at all. It's carnival music The words are creepy enough and augmented by the choice of musical instruments and melody, but at the same time, the song is really just about having fun. As if the Black Rider doesn't want to really harm the person they are with, but cannot help hoping to.
This is also a song that only Waits could write so well. In the hands of a lesser musical artist, the theme and style would be too much but Waits deftly creates three minutes and 21 seconds of perfection. You will never forget the song and will want to listen to the track for the rest of your life trying to find out exactly what it is all about.