Thank you Robin and DJF for your kind help!

I made some experiments that I post here so that other can take advantages
of them or improve them. Attached the output result.

%overlapping fingering
\version "2.19.81"
\fixed c' {
  \set fingeringOrientations = #'(left) \set stringNumberOrientations =
#'(left)
  <g-2 b\3 d'\4>1
}

%reducing fingering size
\version "2.19.81"
\fixed c' {
  \set fingeringOrientations = #'(left) \set stringNumberOrientations =
#'(left)
  \override Fingering.font-size = #-9 \override StringNumber.font-size = #-9
  <g-2 b\3 d'\4>1
}

%reducing fingering size, blanking staff lines, padding fingering to
horizontally align it to stringNumber
\version "2.19.81"
\fixed c' {
  \override Fingering.whiteout = ##t  \override StringNumber.whiteout = ##t
  \override Fingering.font-size = #-9 \override StringNumber.font-size = #-9
  \set fingeringOrientations = #'(left) \set stringNumberOrientations =
#'(left)
  \override Fingering.padding = #0.8
  <g-2 b\3 d'\4>1
}

% moving fingering using Y-offset and X-offset
\version "2.19.81"
\fixed c' {
  \set fingeringOrientations = #'(left) \set stringNumberOrientations =
#'(left)
  <g-\tweak Y-offset -0.8 \tweak X-offset -1.7 -2 b\3 d'-\tweak Y-offset
0.8 \4 >1
}

% moving fingering using Y-offset and padding
\version "2.19.81"
\fixed c' {
  \set fingeringOrientations = #'(left) \set stringNumberOrientations =
#'(left)
  \override Fingering.padding = #0.8
  <g-\tweak Y-offset -0.8 -2 b\3 d'-\tweak Y-offset 0.8 \4 >1
}

% moving fingering using Y-offset and X-offset and blanking staff lines
\version "2.19.81"
\fixed c' {
  \override Fingering.whiteout = ##t
  \override StringNumber.whiteout = ##t
  \set fingeringOrientations = #'(left)
  \set stringNumberOrientations = #'(left)

  <g-\tweak Y-offset -0.8 \tweak X-offset -1.7 -2 b\3 d'-\tweak Y-offset
0.8 \4 >1
}
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