There are many aspects in the example document that need to be straightened:
\documentclass[10pt,english,greek,BCOR=20mm, footnoterule,
lists=totoc, index=totoc, captions=bottombeside, open=any,
iso-8859-7,latin9,utf8]{scrbook}
\usepackage[LGRx,T1,LGR]{fontenc} % define LGR and T1 encodings
\usepackage[utf8]{inputenc} % standard UTF-8 input encoding
\usepackage[english,greek]{babel}
\usepackage[a4paper]{geometry}
\geometry{tmargin=20mm,bmargin=30mm,lmargin=30mm,rmargin=30mm}
\usepackage{color}
\usepackage{units}
\usepackage[normalem]{ulem}
\usepackage[k-loose]{minitoc} % loose line spaced minitoc
\mtcsettitle{minitoc}{} % for empty title
\mtcsetrules{minitoc}{off} % turn off rules before and after the minitoc's
\mtcsetpagenumbers{minitoc}{off} % turn off page numbering in minitoc's
\usepackage[unicode=true,bookmarks=true,bookmarksnumbered=true,
bookmarksopen=true,bookmarksopenlevel=1,breaklinks=true,
pdfborder={0 0 0},backref=page,colorlinks=true]{hyperref}
\usepackage{bookmark} % pdf bookmarks
\hypersetup{pdftitle={Αναφορά...},
pdfauthor={Νίκος Αλεξανδρής},
pdfsubject={Υλοποίηση...},
pdfkeywords={minitoc, greek, english, babel, unicode, LaTeX},
linkcolor=blue, anchorcolor=red, pdfstartview={FitH},
hyperfootnotes=false, unicode=true}
\usepackage{kerkis} % fonts
\usepackage[final,expansion=true,protrusion=true]{microtype} % kerning/margin
\newcommand{\code}[1]{\texttt{#1}} % Textclass specific LaTeX commands
\definecolor{lightgray}{gray}{0.2} % define lightgray
%%% Important!
\addto\extrasenglish{\def\encodingdefault{T1}\fontencoding{T1}\selectfont}
\begin{document}
\dominitoc
\title{\foreignlanguage{english}{An english minitoc-entry in an LGRX encoded document}}
\subtitle{\foreignlanguage{english}{A (not exactly Minimal) Working Example!}}
\author{του Νίκου Αλεξανδρή%
\thanks{\foreignlanguage{english}{\protect\href{mailto:nik@}{nik@}}}}
\maketitle
\tableofcontents
\chapter{Σχεδιασμός~και υλοποίηση}
\minitoc
\section{Δομή εγγράφου\label{sec:a}}
\section{Δομή σελίδας\label{sec:b}}
\begin{otherlanguage*}{english}
\begin{itemize}
\item \foreignlanguage{greek}{(ύψος κειμένου)}
$textheight:\,\unit[438]{pt}*\unit[0.3515]{mm}=\unit[153.957]{mm}$
\item \foreignlanguage{greek}{(πλάτος κειμένου)}
$textwidth:\,\unit[746]{pt}*\unit[0.3515]{mm}=\unit[262.219]{mm}$
\item
$\nicefrac{textwidth}{2}:\,\nicefrac{\unit[746]{pt}*\unit[0.3515]{mm}}{2}=\unit[131.1095]{mm}$
\end{itemize}
\end{otherlanguage*}
\subsection{Κεφαλίδες~και Υποσέλιδες~σημειώςεις}
\begin{otherlanguage*}{english}
\begin{itemize}
\item \sout{use }\emph{\sout{scrpage2}}\sout{ instead of }\emph{\sout{fancyheader}} (see also:
\href{http://tex.stackexchange.com/questions/11220/replacing-fancyhdr-with-scrpage2}%
{tex.stackexchange.com/questions/11220/replacing-fancyhdr-with-scrpage2})
\end{itemize}
\end{otherlanguage*}
\subsection{Δομή πλάγιων σελίδων}
(=\foreignlanguage{english}{landscape})
\begin{otherlanguage*}{english}
\begin{itemize}
\item balance up with respect to page width!
\item in each landscape page: 2x 48\% column width(ed) boxes
\item inside column-boxes: vertically stacked, and centered, 2x photos sized
49\% of text height
\end{itemize}
\end{otherlanguage*}
\section{\texorpdfstring{\foreignlanguage{english}{Thumb index}}{Thumb
index}}
\label{Section: Thumb - Index}
\begin{otherlanguage*}{english}
\begin{itemize}
\item using \code{chapterthumbs.sty}
by Markus Kohm (e.g., among other places also to be found at
\href{file:http://www.tex.ac.uk/tex-archive/info/examples/KOMA-Script-3/Anhang-B/source/chapterthumb.sty}%
{http://www.tex.ac.uk/tex-archive/info/examples/KOMA-Script-3/Anhang-B/source/chapterthumb.sty})
\end{itemize}
\end{otherlanguage*}
\end{document}
Explicit usage of \selectlanguage is seldom needed. The definition you give of \textgreek is useless, as Greek is the default language. It's conversely needed a similar trick for the English text.
Inputting σ and ς directly is obviously possible.
