Normally the argument to \multirow is set ragged right. However, you have packed the text inside a \parbox, which will try to spread the text to the given width. Instead of using \parbox make use of the width argument of \multirow. The syntax is
\multirow{nrows}{width}{text}
You have use width=* which says use the natural width of text, but put text=\parbox{2.5cm}{....}. Instead you can write
\multirow{nrows}{2.5cm}{....}
This fixes the issues in your middle column.
In the first column, the problem is the rules you are adding, your commands \nsr or \dsr. These occur in the first line of text in a paragraph, and so are adding depth to that line, pushing it away from the next line of the paragraph. My guess is that you have placed these rules to help space out the table. In your case it is only necessary to have them at one point in the row, so just add them to say the final column that will not have multiple lines.
If you wish to colour the rows then you need to put the \multirow in its bottom row and specify a negative nrows. Additionally, since you rows are unusually high/deep you will have to add an adjustment:
\multirow{nrows}{width}[adjust]{test}
There will also be problems with colours of the rules. You can use the \hhline suggestion from Cellcolor overwrites partial horizontal lines (\cline).

\documentclass[11pt,table,a5paper]{article}
\usepackage{array,ragged2e}
\usepackage[framemethod=TikZ]{mdframed}
\usepackage[top=2cm, bottom=2cm, outer=1cm, inner=2.1cm, twoside, headsep=26pt]{geometry}
\usepackage{longtable}
\usepackage{multirow}
\begin{document}
\newcommand{\nsr}{\rule[-1.3cm]{0pt}{2.2cm}}
\newcommand{\dsr}{\rule[-3.5cm]{0pt}{4cm}}
{\small
\renewcommand{\arraystretch}{1.8}
\begin{longtable}{|p{2.7cm}|p{1.0cm}|p{2.4cm}|p{1.0cm}|p{1.3cm}|p{0.8cm}|}
\hline
\rowcolor{green} \textbf{\textcolor{white}{ColA}} &\textbf{\textcolor{white}{ColB}} &\textbf{\textcolor{white}{ColC}} &\textbf{\textcolor{white}{ColD}} &\textbf{\textcolor{white}{ColE}} &\textbf{\textcolor{white}{ColF}} \\
\endhead
\hline
\rowcolor[RGB]{243,182,185}
Brainy Person & 3.38&
\multirow{1}{2.5cm}{\textcolor{black}{This is Very first line\\[2ex]
This is Second line\\[2ex]
This is IIIrd line}}
&2.36 & 0.62 & \dsr 18 \\
\hline
Kingestionisation Quesiton Queeneinsteen & 1.46&
\multirow{3}{2.5cm}{\textcolor{black}{This is First line\\[2ex]
This is Second line\\[2ex]
This is Third line\\[2ex]
This is Fourth line}}
& 1.02 & 0.62 & \nsr 13 \\\cline{1-2} \cline{4-6}
Foolish Person & 1.16 &
& 0.81 & 0.62 & \nsr 45 \\\cline{1-2} \cline{4-6}
Attacking Person Rob & 1.02 &
& 0.71 & 0.52 & \nsr 31 \\\cline{1-2} \cline{4-6}
\hline
\rowcolor{red}
Datset
& 24
& \multicolumn{2}{c|}{Normal Value}
& 23
& 342 \\
\hline
\end{longtable}}
\end{document}
You should beware of extra spaces that were in the code for your headings (\textbf{ Col}), these were causing bad alignment.
If you want the first column ragged right, then you can start the table format specification with {|>{\raggedright}p{2.7cm}... instead of just {p{2.7cm}....
If none of your cells are guaranteed to be single rows you could add a separate column to hold the rules.

\documentclass[11pt,table,a5paper]{article}
\usepackage{array,ragged2e}
\usepackage[framemethod=TikZ]{mdframed}
\usepackage[top=2cm, bottom=2cm, outer=1cm, inner=2.1cm, twoside, headsep=26pt]{geometry}
\usepackage{longtable}
\usepackage{multirow}
\usepackage{hhline}
\begin{document}
\newcommand{\nsr}{\rule[-1.3cm]{0pt}{2.2cm}}
\newcommand{\dsr}{\rule[-3.5cm]{0pt}{4cm}}
{\small
\setlength{\arrayrulewidth}{1pt}
\setlength{\minrowclearance}{1pt}
\renewcommand{\arraystretch}{1.8}
\begin{longtable}{|p{2.7cm}|p{1.0cm}|p{2.4cm}|p{1.0cm}|p{1.3cm}|p{0.8cm}|}
\hline
\rowcolor{green} \textbf{\textcolor{white}{ColA}} &\textbf{\textcolor{white}{ColB}} &\textbf{\textcolor{white}{ColC}} &\textbf{\textcolor{white}{ColD}} &\textbf{\textcolor{white}{ColE}} &\textbf{\textcolor{white}{ColF}} \\
\endhead
\hline
\rowcolor[RGB]{243,182,185}
Brainy Person & 3.38&
\multirow{1}{2.4cm}[-6pt]{\textcolor{black}{This is Very first line\\[2ex]
This is Second line\\[2ex]
This is IIIrd line}}
&2.36 & 0.62 & \dsr 18 \\
\hline
\rowcolor{teal}
Kingestionisation Quesiton Queeneinsteen & 1.46&
& 1.02 & 0.62 & \nsr 13 \\
\hhline{-->{\arrayrulecolor{teal}}->{\arrayrulecolor{black}}|---}
\rowcolor{teal}
Foolish Person & 1.16 &
& 0.81 & 0.62 & \nsr 45 \\
\hhline{-->{\arrayrulecolor{teal}}->{\arrayrulecolor{black}}|---}
\rowcolor{teal}
Attacking Person Rob & 1.02 &
\multirow{-3}{2.4cm}[80pt]{\textcolor{black}{This is First line\\[2ex]
This is Second line\\[2ex]
This is Third line\\[2ex]
This is Fourth line}}
& 0.71 & 0.52 & \nsr 31 \\\cline{1-2} \cline{4-6}
\hline
\rowcolor{red}
Datset
& 24
& \multicolumn{2}{c|}{Normal Value}
& 23
& 342 \\
\hline
\end{longtable}}
\end{document}
fixuparugement. Then there is a problem colouring the rules. See http://tex.stackexchange.com/q/65231/15925 for most of this. – Andrew Swann Aug 22 '13 at 08:12-6ptshould be the same in any one such cell. The80ptis a linear function of the number of rows minus the height of the text you are inserting; this is because you have fixed the row heights. – Andrew Swann Sep 10 '13 at 14:47