How to combine \ifdefstring (etoolbox) with \multicolumn

The problem is that \ifdefstring is not expandable, therefore it cannot be used at this place of a table. You can overcome this by using the low-level \ifx:

\documentclass[10pt,a4paper,twoside]{article}
\usepackage{etoolbox}
\usepackage{booktabs}

\newcommand{\ReportLanguage}{no}
% two alternative values for \ReportLanguage: 
% "no" for norwegian and "en" for english
\newcommand{\NorwegianLanguage}{no}

\begin{document}
\begin{tabular}{ccc}
      \ifx\ReportLanguage\NorwegianLanguage
          \multicolumn{2}{c}{Utslippspunkt} & Salinitet  \\       
             Dybde & temperatur                &             \\
      \else
          \multicolumn{2}{c}{Release point}  & Salinity  \\                           
            Depth & temperature                &            \\
      \fi
            \midrule
            100 & 10 & 32 \\
            150 & 7  & 33 \\            
            180 & 4  & 35 \\
            \bottomrule
\end{tabular}
\end{document}

At a beginning of a table cell/line, LaTeX looks for things like \multicolumn, \hline etc. When you put something non-expandable there, LaTeX simply stops looking for these things. And if they are found later (like your \multicolumn), LaTeX is confused and throws an error.

Just a remark: I think you want twoside instead of twosided (maybe both work, I dunno, I always use the first one).

---

If you don't want to define \NorwegianLanguage, you can do this (USE AT YOUR OWN RISK):

\documentclass[10pt,a4paper,twosided]{article}
\usepackage{etoolbox}
\usepackage{booktabs}

\newcommand{\ReportLanguage}{no}
% two alternative values for \ReportLanguage: 
% "no" for norwegian and "en" for english

\begin{document}
\begin{tabular}{ccc}
      \expandafter\ifx\csname\ReportLanguage LANGUAGE\endcsname\noLANGUAGE
          \multicolumn{2}{c}{Utslippspunkt} & Salinitet  \\       
             Dybde & temperatur                &             \\
      \else
          \multicolumn{2}{c}{Release point}  & Salinity  \\                           
            Depth & temperature                &            \\
      \fi
            \midrule
            100 & 10 & 32 \\
            150 & 7  & 33 \\            
            180 & 4  & 35 \\
            \bottomrule
\end{tabular}
\end{document}

I'd use a more user-friendly approach: you issue a \TableHeader command that contains a key-value list of the headers you want for the next table, then in the table you place \UseTableHeader.

In the example I switch language (which probably you don't want to do in a real document) just to show the result; notice that the values given as argument to \TableHeader survive until another \TableHeader is issued again.

\documentclass[10pt,a4paper,twoside]{article}
\usepackage{booktabs}
\usepackage{keyval}

\makeatletter
\define@key{espentable}{no}{\def\espen@header@no{#1}}
\define@key{espentable}{en}{\def\espen@header@en{#1}}

\newcommand{\TableHeader}[1]{%
  \setkeys{espentable}{#1}%
  \ignorespaces
}
\newcommand{\UseTableHeader}{\@nameuse{espen@header@\espen@language}}

% two alternative values for \ReportLanguage: 
% "no" for norwegian and "en" for english
\newcommand{\ReportLanguage}[1]{\def\espen@language{#1}}
\def\espen@language{en}% default
\makeatother

\ReportLanguage{no}

\begin{document}

Norsk:

\TableHeader{
  no={\multicolumn{2}{c}{Utslippspunkt} & Salinitet \\
      Dybde & temperatur                &           \\},
  en={\multicolumn{2}{c}{Release point}  & Salinity \\                           
      Depth & temperature                &          \\}
}
\begin{tabular}{ccc}
\toprule
\UseTableHeader
\midrule
100 & 10 & 32 \\
150 & 7  & 33 \\            
180 & 4  & 35 \\
\bottomrule
\end{tabular}

\bigskip

English:

\ReportLanguage{en}
\begin{tabular}{ccc}
\toprule
\UseTableHeader
\midrule
100 & 10 & 32 \\
150 & 7  & 33 \\            
180 & 4  & 35 \\
\bottomrule
\end{tabular}

\end{document}

This has the advantage that it's easily extendable to more than two languages.