In what situations would someone use one of the following forms over the
others when requesting the action やる?

  1. やってくれる?
  2. やってくれない?
  3. やってくれ
  4. やって(ください)

My assumption is that the first two would translate more along the lines of
"Could you do it?" while the last two would translate to "Please do it." (Am I
correct?) But between (1) and (2) and between (3) and (4), what are the
differences?
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2018-01-22T02:26:35.010
56111
2018-09-29T22:01:12.713
23869
question
usage nuances giving-and-receiving
Different inflectional forms of くれる
Not 'can', but 'will'.

  1. Would you do it (for me)? (Spoken by a girlfriend, close female relation)
  2. Won't you do it (for me)? (Spoken by friends, classmates, co-workers) 
  3. Please do it [gruff]. (Spoken by authority figures)
  4. Please do it [straight]. (Same as 3, with a slight attempt to not sound so gruff)

There is no great substantive difference in meaning between (1) and (2). (1)
just sounds more cutesy. (3) sounds bossy or angry, while (4) just sounds
'direct'.

For (4), you wrote やって（ください）. If we are assuming that only やって is uttered, it
is yet more direct and aggressive than やってくれ, but not as much so as やれ.
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2018-01-22T03:27:52.563
56112
2018-02-01T16:14:33.793
2018-02-01T16:14:33.793
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answer