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.
Since you want ToCs in sections, you would have to use \dosecttoc, and \secttoc, instead of \doparttoc and \parttoc.
However, the minitoc documentation says that section ToCs are not available for the report and book classes. minitoc will only give ToCs for the highest sectioning commands in the hierarchy of the class. So I guess, no luck here with this package.
Best Answer
Here's one possible solution using the
titletocpackage; the idea is to use\addcontentslinewith extensionptc(the default extension used bytitletocfor the partial ToCs) to include information in the partial ToC only:An image of the general ToC:
An image of the partial ToC at the beginning of the chapter: