Before version 7, WinEdt do not use Unicode as internal working encoding. The UTF-8 support from WinEdt 5.5 to WinEdt 6.0 is partial: WinEdt can read a UTF-8 file and then convert it to local encoding, the editor works in the local non-unicode encoding, and then you can save the file in UTF-8 encoding.
For users, it means that, as Ulrike Fischer said, you can only use the characters from your own codepage. Say, I can use 中文
on my Windows system (codepage 936), but the same file may be broken on your Windows system (codepage 1251). That's the problem.
If you use only one input encoding, say, cp1251, cp866 or koi8-r, you don't need the full support of Unicode, WinEdt 6 is fine.
If you want to typeset this, you need new WinEdt 7:
% XeLaTeX
\documentclass{article}
\usepackage{xeCJK,arabxetex}
\setmainfont{Times New Roman}
\newfontfamily\arabicfont[Script=Arabic]{Times New Roman}
\setCJKmainfont{SimSun}
\begin{document}
English, la langue française, 中文, русский язык, Ελληνικά
\begin{arab}
اللغة العربية
\end{arab}
\end{document}