In "ordinary LaTeX" you can use
\documentclass{article}
\usepackage[T2A,LGRx,T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[greek,russian,polish]{babel}
\begin{document}
Cześć ludzie
\foreignlanguage{russian}{привет мир}
\foreignlanguage{greek}{Γεια σας κόσμο}
\end{document}
This needs TeX Live 2012 (or an up-to-date MiKTeX); with older distributions, remove LGRx and use utf8x as option to inputenc.
With TeX Live 2011 at the latest version, one can use the same method, but due to an error in the packaging of files the following trick in the preamble is needed:
\makeatletter
\input{/usr/local/texlive/2011/texmf-dist/doc/latex/lgrx/lgrenc.dfu}
\makeatother