I get the Trashmen and the Shadows of Night mixed up...
The Shadows of Night were one of many bands to record a cover of Gloria.
The Trashmen merged The Bird’s The Word with Papa Oom Mow Mow (both by the Rivingtons) and somehow got labelled a midWest “surf” band. Later Surfin Bird was covered by the Cramps and the Ramones (who sought approval from the Cramps to likewise cover the song).