"Weng" syllables rhyme with the fnal -ong
In the second paragraph, what does end refer to? 


When I speak, I tends to do something like this /wʊ-ɤŋ/. I have never noticed this behavior before. For the word 老翁 (old man), if you say it either way: /lɑʊ.wʊŋ/, /lɑʊ.wəŋ/, /lɑʊ.wɤŋ/, /lɑʊ.wʊəŋ/, etc, they are all interpreted as the same word, thus "free variations". This depends on the individual accent.

I have never studied rhymes seriously before, so if your book says "weng" rhymes with "tong", then they must be using the /wʊŋ/ way of speaking. For example: 通風 (air circulation) may be pronounced as /tʊŋ.fʊŋ/ or /tʊŋ.fɤŋ/, but never as /tɤŋ.fɤŋ/. I personally say /tʊŋ.fɤŋ/. 

As for your last quote, I don't understand how the free variation has complementary distribution.