mycmd-[options1]{action1}
mycmd+[options2]{action2}
mycmd/[options3]{action3}

documentclass{article}
newcommandmycmd[1]{defmycase{#1}mycmdaux}
newcommandmycmdaux[2][]{Case is ``mycase'', options are ``#1'' and action is ``#2''}

begin{document}
mycmd-[options1]{action1}

mycmd+[options2]{action2}

mycmd/[options3]{action3}
end{document}

documentclass{article}

begingroup
makeatletter
@firstofone{%
  endgroup
  %%-------------------------------------------------------------------------
  %% Check whether argument is empty:
  %%.........................................................................
  %% @CheckWhetherNull{<Argument which is to be checked>}%
  %%                   {<Tokens to be delivered in case that
  %%                     argument which is to be checked is empty>}%
  %%                   {<Tokens to be delivered in case that
  %%                     argument which is to be checked is not empty>}%
  newcommand@CheckWhetherNull[1]{%
    expandafter@secondoftwostring{expandafter@secondoftwo
    expandafter{expandafter{string#1}expandafter@secondoftwo
    string}expandafter@firstoftwoexpandafter{expandafter
    @firstoftwoexpandafter@secondoftwoexpandafter}string
    }@firstoftwo
  }%
  %%-------------------------------------------------------------------------
  %% Check whether argument contains no exclamation-mark on top-brace-level:
  %%.........................................................................
  %% @CheckWhetherNoExclamationMark{<Argument which is to be checked>}%
  %%                   {<Tokens to be delivered in case that
  %%                     argument which is to be checked does not contain !>}%
  %%                   {<Tokens to be delivered in case that
  %%                     argument which is to be checked does contain !>}%
  newcommand@RemoveToExclamationMark{}%
  longdef@RemoveToExclamationMark#1!{}%
  newcommand@CheckWhetherNoExclamationMark[1]{%
    expandafter@CheckWhetherNullexpandafter{@RemoveToExclamationMark#1!}%
  }%
  %%-------------------------------------------------------------------------
  %% Fork depending on minus, plus, slash, something else.
  %%.........................................................................
  %% (First via kernek@ifnextchar check whether the next token is an
  %%  opening brace.
  %%  If it is, we know that it is neither a minus nor a plus nor a slash.
  %%  If it is not, it can be processed as an undelimited macro-argument
  %%  where under normal catcode-régime brace-stripping cannot occur, thus
  %%  in this ase use mycmd@furthercheck for checking for
  %%  minus/plus/slash/something else.
  %%  Make the command robust as due to the not fully expandable
  %%  kernel@ifnextchar it should not be carried out in
  %%  pure-expansion-contexts.)
  newcommandmycmd{}%
  DeclareRobustCommandmycmd{%
    kernel@ifnextcharbgroup
                      {mycmd@else}%<-Next token is opening brace or bgroup,
                                   %  thus something other than minus/plus/slash.
                      {mycmd@furthercheck}%<-Check for minus/plus/slash.
  }%
  %
  newcommand@mycmdfork{}%
  longdef@mycmdfork#1!!-!+!/!#2#3!!!!{#2}%
  %
  newcommandmycmd@furthercheck[1]{%
    @CheckWhetherNoExclamationMark{#1}{%
      @mycmdfork
      !#1!-!+!/!{mycmd@else#1}%<-Else #1 empty (actually this can't happen.)
      !!#1!+!/!{mycmd@minus}%<-minus
      !!-!#1!/!{mycmd@plus}%<-plus
      !!-!+!#1!{mycmd@slash}%<-slash
      !!-!+!/!{mycmd@else#1}%<-ELSE no exclamation-mark
      !!!!%
    }{mycmd@else#1}%<-ELSE Exclamation-mark
  }%
  newcommandmycmd@minus[2][Optional argument's default at minus]{%
    Case minus-sign:\%
    Optional argument is: texttt{#1}\%
    Mandatory argument is: texttt{#2}%
  }%
  newcommandmycmd@plus[2][Optional argument's default at plus]{%
    Case plus-sign:\%
    Optional argument is: texttt{#1}\%
    Mandatory argument is: texttt{#2}%
  }%
  newcommandmycmd@slash[2][Optional argument's default at slash]{%
    Case slash-sign:\%
    Optional argument is: texttt{#1}\%
    Mandatory argument is: texttt{#2}%
  }%
  newcommandmycmd@else[2][Optional argument's default at other cases]{%
    Some other case:\
    Optional argument is: texttt{#1}\%
    Mandatory argument is: texttt{#2}%
  }%
}%

pagestyle{empty}

begin{document}

vspace*{-1.33in}%
parskip=baselineskip
parindent=0pt
enlargethispage{1in}%
footnotesize

verb|mycmd X| yields:\
mycmd X

verb|mycmd!| yields:\
mycmd!

verb|mycmd{!}| yields:\
mycmd{!}

verb|mycmd{-}| yields:\
mycmd{-}

verb|mycmd{+}| yields:\
mycmd{+}

verb|mycmd{/}| yields:\
mycmd{/}

verb|mycmd{Some other case without given optional argument}| yields:\
mycmd{Some other case without given optional argument}

verb|mycmd[Given optional argument]{Some other case with given optional argument}| yields:\
mycmd[Given optional argument]{Some other case with given optional argument}

verb|mycmd+{Plus case without given optional argument}| yields:\
mycmd+{Plus case without given optional argument}

verb|mycmd+[Given optional argument]{Plus case with given optional argument}| yields:\
mycmd+[Given optional argument]{Plus case with given optional argument}

verb|mycmd-{Minus case without given optional argument}| yields:\
mycmd-{Minus case without given optional argument}

verb|mycmd-[Given optional argument]{Minus case with given optional argument}| yields:\
mycmd-[Given optional argument]{Minus case with given optional argument}

verb|mycmd/{Slash case without given optional argument}| yields:\
mycmd/{Slash case without given optional argument}

verb|mycmd/[Given optional argument]{Slash case with given optional argument}| yields:\
mycmd/[Given optional argument]{Slash case with given optional argument}

end{document}