Songs about radio, in no particular order, last revision 20210727
Many are on YouTube.

Freddy Cannon | Transistor Sister
Alma Cogan | Just Couldn't Resist Her With Her Pocket Transistor
Mark Dinning | Top 40, News, Weather and Sports
Freddy Cannon | The Dedication Song
Terry Lee Jenkins | Boston My Home Town (WCOP promo, 1961)
Jonathan Richman & Modern Lovers | Roadrunner
Private Lightning | Physical Speed
Wall of Voodoo | Mexican Radio
Harry Chapin | W.O.L.D.
Lou Reed & Velvet Underground | Rock and Roll
Buggles | Video Killed the Radio Star
Golden Earring | Radar Love
R.E.M. | Radio Free Europe
R.E.M. | What's the Frequency Kenneth?
R.E.M. | Radio Song
Guess Who | Clap for the Wolfman
Sass | Radio
Kinks | Around the Dial
Van Morrison | Caravan (Turn up your Radio)
Van Morrison | Wavelength
Van Morrison | In the Days Before Rock and Roll
Reunion | Life is a Rock (But the Radio Rolled Me)
George Carlin | Wonderful WINO (Top-40 Disc Jockey)
Everclear | AM Radio
Joe Jackson | On Your Radio
Queen | Radio Gaga
Ramones | Do You Remember Rock 'n' Roll Radio
Ramones | We Want the Airwaves
Elvis Costello | Radio Radio
Elvis Costello | Radio Sweetheart
Corrs | Radio
Clash | This is Radio Clash
Clash | London Calling
Clash | Capital Radio One
Pearls Before Swine | Dear Miss Morse
Rush | The Spirit of Radio
Donna Summer | On the Radio
Al Stewart | Song on the Radio
Smash Mouth | Radio
Autograph | Turn On Your Radio
Doors | The Wasp (Texas Radio and the Big Beat)
Beach Boys | Magic Transistor Radio
Joni Mitchell | You Turn Me On I'm a Radio
Kendalls | Thank God for the Radio
Wolfe Tones | Radio Toor-I-Li-Ay
Dinah Washington | TV Is the Thing This Year
Charlie Dore | Pilot of the Airwaves
k.d. lang | Tune Into My Wave
Steely Dan | FM (No Static at All)
Donald Fagen | The Nightfly
Anthony & the Sophomores | Play Those Oldies Mr DJ
Bruce Springsteen | Radio Nowhere
Ashton Sheperd | Rory's Radio
Electric Light Orchestra | Mr. Radio
Tangerine Dream | Radio City
Tom Petty | The Last DJ
Jethro Tull | Radio Free Moscow
Marshall Crenshaw | Radio Girl
Jesse Malin | Broken Radio
Carpenters | Yesterday Once More
B52's | Planet Claire (with Morse code)
Dire Straits | Telegraph Road
Five Americans | Western Union
Don Bowman | Hello DJ
Sixpence None The Richer | Radio
The 102.1 Band | Working on the Radio
Orchestral Manoeuvres in the Dark (OMD) | Radio Prague; Time Signals; Swiss Radio International; Radio Waves
Butter Beans and Suzie | Radio Papa, Broadcasting Mama
Warren Zevon | Mohammed's Radio
Reba McIntire | On the Radio 
Stiff Little Fingers | You Can't Say Crap On The Radio
Eric Idle / Monty Python | I'll Bet You They Won't Play This Song on the Radio
Karlheinz Stockhausen | Kurzwellen (Radio Bremen Aufname), Teil I (1/2)
George Harrison | Devil's Radio
Toby Keith | How Do You Like Me Now?! (Living in Your Radio)
David Bowie | TVC 15 (Transmission)
ZZ Top | Heard It On The X
Indeep | Last Night A DJ Saved My Life
L.L. Cool J | I Can't Live Without My Radio
Nazareth | Turn On Your Receiver
Atmospherics | Listen To The Radio
Pukka Orchestra | Listen To The Radio
Fortunes | Caroline
Robert Glasper Experiment | Black Radio
Ham Band | Come and Join Us on the Airwaves
Frank Zappa | The Radio is Broken
Blue Peter | Radio Silence
Boris Grebenshikov | Radio Silence
Jim Johnston | Oh Radio
Kathleen Edwards | One More Song the Radio Won't Play
Journey | Raised on Radio
Rush | The Pass
Tiffany | Radio Romance
George Jones | Radio Lovers
Jimmy Buffett | Homemade Music (ain't on the radio)
Patti Smith | Radio Ethiopia
Lolly | Viva La Radio
Roger Waters | Radio K.A.O.S.
Harry Nilsson | Turn On Your Radio
Korn  | Twisted Transistor
C.W. McCall | Convoy
Beach Boys | Mount Vernon and Fairway
Blasters | Border Radio
Contrast | Wireless Days
Jimi Hendrix Experience | Radio One Theme
Martha & the Muffins | Black Stations White Stations
Nirvana | Radio Friendly Unit Shifter
Ravyns | Raised on the Radio
Watchmen | Stereo
Borgy's Banjo Reunion | Radio
Al Jolson | Mr. Radio Man (1920s)
Vincent Lopez & His Orchestra | Kiss Me By the Wireless (1920s)
Henry Hall & His Orchestra | On the Air (1930s, Britain)
Ray Stevens | Turn Your Radio On (Get in Touch with God)
Gene Krupa | Disc Jockey Jump
Chuck Berry | Roll Over Beethoven
Cheap Trick | On the Radio
Spoon | Car Radio
Dixie Foust Taffy | I Love My Radio
Replacements | Left of the Dial
Mark Cohn | Listening to Levon
Rage Against the Machine | Guerrilla Radio
Toasters | Pirate Radio
John Hiatt | Pirate Radio
Mojo Nixon and Skip Roper | Pirate Radio
Alkaline Trio | Radio
Beyoncé | Radio
Mary Black | Late Night Radio
Erin Bode | With The Radio On
Donnas | Gimme My Radio
Steve Earle | Satellite Radio
Kathleen Edwards | One More Song the Radio Won't Like
Fishbone | ? (Modern Industry)
Nanci Griffith | Listen To The Radio
John Hartford | Turn Your Radio On
Hole | Boys On The Radio
Stan Kenton and His Orchestra | Intermission Riff
Les Reed Orchestra | Man Of Action
Roaring 60s | We Love the Pirates
Tennis Shoes | (Do the) Medium Wave
Joyce Hahn with the VE2QR Orchestra featuring VE2BR, F9KT | CQ Serenade (Three versions: English, French, Instrumental)
Peter Gabriel | On the Air
Charly McClain | Sleepin' With The Radio On
Charly McClain | Radio Heart
Lionel Cartwright | I Watched It All On My Radio
Kathy Mattea | Listen to the Radio
Todd Rundgren | Wolfman Jack
Arbogast and Ross | CHAOS
George Clinton | Loopzilla (WBLS, don't touch that radio, don't touch that knob!)
Mighty Mike Shermer Band | My Big Sister's Radio
Smashing Pumpkins | I of the Mourning
Blue Oyster Cult | Dominance and Submission
Starbuck | Moonlight Feels Right
Meat Loaf | Paradise by the Dashboard Light
Long Tall Ernie & The Shakers | Turn the Radio On
Selecter | On My Radio
Plain White T's | Radios In Heaven
Ballboy | The Guide To The Short Wave Radio
Jimi Hendrix | Radio One
Joy of Cooking | Morning Man
Toni Brown & Terry Garthwaite | Morning Man
Nikita The K | Go Go Radio Moscow
Dickie Goodman | Berlin Top Ten
Who | Who Sell Out (complete 1967 LP inspired by UK pirate radio. Has top-40 style jingles and adverts)

Special mention:
Wilco's album Yankee Hotel Foxtrot gets its name from a recording of an Israeli shortwave numbers station provided by The Conet Project. The title is repeated by a female voice in the song “Poor Places”.