Are many of the wr- words effects of the common cause of the PIE wer- root? Obviously. Was there some kind of onomatopoeic cause of the wer- root having the meaning of turning? Perhaps it could have been the twisting up of the mouth to make the more emphatic -r- sound, but that's just silly speculation (silliness never stopped me before).
Larry, if I understand you correctly, you're asking if the sounds of the *wer- root were onomatopoeic in origin. Both in the case of PIE and English, I don't think so.
There are 13 reconstructed roots in the form *wer- in Pokorny's dictionary (Indogermanisches Etymologisches Wörterbuch. This is the standard reference in the field and is quoted by page number in the Indo-European Roots appendix (by Calvert Watkins at Harvard) in the American-Heritage Dictionary (online and in print). These roots and their meanings are:
1. wer- 'to bind, fasten, join; suspend; (in weighing also) heavy; line, cord'
2. wer- 'elevated place'
3. wer- 'to turn, twist; bend, curve'; this is our root with more than seven pages for the entry.
4. wer- 'to find, discover; take'
5. wer- 'to close, cover, lock; protect; save, rescue'
6. wer- 'to say or speak (solemnly)' : our word word is from this root wr-dho-
7. wer- 'to tear, rip; scratch'
8. wer- 'to perceive, be aware of; pay attention, heed'
9. wer- adj. 'wide, broad'
10. wer- 'river; to flow'
11. wer- 'to prove one's friendship'
12. wer- 'to burn, scorch'
13. wer- 'squirrel'
So, at least in PIE, there were a lot of roots that didn't mean twist, many of which did not leave a trace in English vocabularywise. But these 13 roots left lots of words in all the other IE languages, which were used to reconstruct the roots and their meanings.
A note about the roots. Any root in PIE, can take a number of shapes, called grades: the e-grade (e.g., *wer), which is the form usually cited in dictionaries, the o-grade, (e.g., *wor-), and the zero-grade (e.g., wr-). It is the zero-grade of wer- that most of the English words in your list come from.
Now, I suppose you could argue that only the words from the third wer- root survived into English because, the Anglo-Saxon, started to associate words beginning in wr- with twisting and surpressed the other words ...
For more info, you might check out the link to Wikipedia on IE languages that I posted earlier in this thread.