How to draw stretched 2D vectors in TikZ?

The rotate around z key can be used to reasonable effect here:

\documentclass[tikz,border=5]{standalone}
\begin{document}
\begin{tikzpicture}[x=(0:1cm), y=(90:1cm), z=(215:1cm / sqrt 2)]
\draw [dashed] (0, 0) -- (0, 0, 10);
\foreach \i [count=\z] in {-20, 0, 20, 40}
\filldraw [fill=gray!50, shift={(0, 0, \z*2)}, rotate around z=\i] 
  (0, 0, -1/2) -- (0, 2, -1/2) -- (0, 2, -1) -- (0, 3, 0) --
  (0, 2, 1) -- (0, 2, 1/2) -- (0, 0, 1/2) -- cycle;
\end{tikzpicture}
\end{document}

Probably you need to fine tune this a little bit, but what you actually could try, is applying an additional slant:

\documentclass[border=5mm,tikz]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usetikzlibrary{calc,shapes.arrows}
%
\begin{document}
    \begin{tikzpicture}[decoration={brace}, every node/.style={anchor=west,draw,single arrow,fill=gray!30}]
        %
    % Line
    \draw[dashed] (-0.8,.125) -- (2,2);
        %
    % Arrows
    \node[rotate=160,xshift=1mm,yshift=-1mm, xslant=0.75] (a) at (-0.25,.425) {\hspace*{0.96cm}};
    \node[rotate=140,xshift=1mm,yshift=-1mm, xslant=0.275] (b) at (0.4,0.8) {\hspace*{1cm}};
    \node[rotate=110,xshift=1mm,yshift=-1mm, xslant=-0.25] (c) at (0.8,1.1) {\hspace*{1.1cm}};
    \node[rotate=90,xshift=1mm,yshift=-1mm, xslant=-0.65] (d) at (1.4,1.5) {\hspace*{1cm}};
        %
\end{tikzpicture}
\end{document}