StreamTheWorld use Flash for the player on the websites, but they don't use Flash streams (which in reality are video streams with audio only).
Their Flash player plays either MP3 or AACplus streams. In the case of WDEL and others, StreamTheWorld only provide AACplus streams in a format that the SoundBridges (and other internet radio devices like the Reciva based ones) can't handle.
StreamTheWorld's audio URLs (.pls and .asx) which you list contain multiple stream URLs so that more listeners can connect to the station (and there are fallback streams, too). The content of both the .pls and .asx files is identical, so there's no need to have them both (.pls usually is the better alternative for the SoundBridge).
The audio URL for WDEL is http://provisioning.streamtheworld.com/pls/WDELAMAAC.pls
. It will play in Winamp and other software players, but not on the SoundBridge.
BTW: StreamTheWorld's (and for example LiquidCompass's) switch to AACplus generally is a good move, because AACplus provides higher quality than MP3 at low bitrates. It's Roku's fault that the SoundBridge only has preliminary support for this audio codec. But that's no longer of any importance, I guess, as the M1001 has finally died and the R1000 will decease soon.