I'm no expert in using
TikZ (which I guess offers by far more tools for creating new symbols), thus I present you my very own
\mapsto command as an example how one can combine existing
LaTeX symbols. First the MWE:
and the resulting symbol:
obviously the vertical bar is longer than for the original
\mapsto but from what you said I assumed that you intend the vertical bars to share the height of the arrowhead.
Now take another look at the MWE, in the definition of the
\mymapsto command I superimposed a
\rightarrow with a
\ooalign see this answer for a quick course on
\ooalign). Obviously there's a lot of work required when determining the correct dimensions of
\raise, however, using my code as basis you should be able to construct the 15 remaining symbols yourself [don't forget
\rotatebox, it will be useful!]. I'd like to stress that you should use the units
ex when constructing a symbol because when doing so the symbols will remain correct for different fontsizes (or so I'm told).
In constract to using
TikZ this solution might be a little less time-consuming, but you won't learn something new in the process I guess...