There are not too many that fit the description. Here is one:
C18 is an high-performance MP3 player with 1.8 inches Screen which can show the relevant information. Built-in 8GB memory capacity ensures you to download your favorite songs freely. And, it supports many audio formats such as, MP3, WMA, AAC, APE, FLAC, WAV, etc and supports TF Card (Up to 128G)...
The best that I can come up with that meets your demands is the following:
Fiio X5 (2nd Gen)
Note, this is not exactly cheap:
Dual Micro SD card Supporting up to 256GB (128GB x 2)
400 x 360
$36 - Android with USB OTG support and OTG Player App
Get the iNOVA EX756 Android Tablet for $36 with the USB Video Player - OTG Player app. Or some other Android tablet or phone with USB OTG support.
Comes with a USB OTG cable, so you can plug in your flash drive (probably doesn't provide enough power to spin up a hard drive, though).
SD slot only goes up ...
If you can spend up to 250 USD and if it doesn't have to be very tiny then I would recommend to look for a smartphone¹. Several apps exist, among them VLC for Android, iOS and Windows Phone. I just tried it on Android which works fine with m3u playlists (I never bothered to try until now and VLC on my Windows Phone somehow doesn't read the same file, even if ...
I'm not sure about dedicated MP3 players but you can buy any cheap prepaid Android phone and use the app of your preference. I really like DoggCatcher, but there are many other podcast apps to choose from.
I recently bought a $15 LG something-or-other prepaid Verizon phone and use it exclusively for podcasts and using email over WiFi.
Some headphones have ...