Pi, Kappa, Latin Small Letter Long S: problems with UTF8

The long s (ſ) is accessible through the TS1 fontencoding.
Depending on the frequency you need it in your text, you can use it

• with the \longs command or
• the "s command.

For written Greek text I'd use the babel package.
For Greek text in verbatim mode you can use the alltt package and either the babel package again or (for single letters) the textgreek package.
_{^{Edit: I just read that you use a customized wideverbatim environment. Can you provide a definition? I coudn't find one.}}

I have troubles with the Greek font encoding LGR.
Someone with a better understanding of font encoding might improve this answer.

\documentclass[graybox,envcountchap,sectrefs]{svmono}

\usepackage[LGR,TS1,T1]{fontenc}
\usepackage[utf8x]{inputenc}

\usepackage{lmodern}
\usepackage[polutonikogreek,english]{babel}
\usepackage{textgreek}
\usepackage{alltt}

\def\longs{{\fontencoding{TS1}\selectfont s}}
\def\greek#1{{\selectlanguage{greek}\fontencoding{LGR}\selectfont #1}}

\catcode`\"=\active%
\def"s{{\fontencoding{TS1}\selectfont s}}
\def\noLongS{\catcode`\"=12}

\begin{document}

\begin{alltt}
   # sin(\textpi * t)
   # sin(\greek{p} * t)
\end{alltt}

\noindent Kudos ({\greek{k~udos}) % κῦδος
\\
long s: Wach\longs tube\\
long s: Wach"stube\\
{\noLongS%
not a long s: Wach"stube}
\end{document}

I was able to compile properly your MWE (although simplified a bit) using the textalpha package instead of textgreek. Here is how :

\documentclass{article}
\usepackage[utf8x]{inputenc} % Note : option utf8 works also
\usepackage[T1]{fontenc}
\usepackage{textalpha}

\begin{document}
\begin{verbatim}
   # sin(π * t)
\end{verbatim}
Kudos (κῦδος)
\end{document}

So I obtain the following result :

(Added:) Please note that the textalpha package seems to give better results than the textgreek one.