Let me explain 歌謡曲 first. Today, 歌謡曲 is a word that refers to "Japanese pop songs roughly in 1930-1970". 昭和歌謡 refers to almost the same thing. Wikipedia defines this like this:
Kayōkyoku (歌謡曲, literally "Pop Tune") is a Japanese pop music genre, which became a base of modern J-pop. The Japan Times described kayōkyoku as "standard Japanese pop" or "Shōwa-era pop".
Kayōkyoku in the narrower and more practical sense, however, excludes
J-pop and enka.
In other words, roughly speaking, 歌謡曲 today is analogous to "oldies" in English-speaking countries. Perhaps this originally used to refer to pop songs in general, but after the word J-pop became popular in 1980's, 歌謡曲 started to refer to older songs. A typical 歌謡曲 is like this. You might find it somewhere between enka and Western music.
As you have noticed, 歌謡 is seldom used outside the contexts related to old Japanese 歌謡曲. In its broader sense, it can still refer to old pop songs in general, especially in academic or technical contexts. For example, some people may use アメリカの歌謡 referring to American oldies in the 60's. You should not use it to refer to songs in general. It's usually odd to call modern hip-hop songs 歌謡.
Related: When do I use all the words meaning "song"?