Nomenclature sorting italic

The sorting is obtained by adding a default prefix a, so the sort key is a\textit{n}. You can override it:

\documentclass[12pt]{report}

\usepackage[intoc]{nomencl}
\renewcommand{\nomname}{List of Abbreviations}
\setlength{\nomlabelwidth}{6cm}
\makenomenclature

\nomenclature{g}{grams(s)}
\nomenclature{abs}{absolute}
\nomenclature{min}{minute(s)}
\nomenclature[an]{\textit{n}}{normal}
\nomenclature{w}{weak}

\begin{document}

\printnomenclature
\tableofcontents

\end{document}

Hint: don't use \include for inputting the list, but \input. In the code above I added the list in the document in order to avoid auxiliary files. The best place is the preamble, in my opinion, so you should use

\input{abbreviations}