Here is The Russian radio (Русское радио). All the songs in Russian. It has on-line broadcast. http://www.rusradio.ru/onlineradio/
You can find some lyric for Russian songs here http://megalyrics.ru/site/songs.htm. There are translation there (mostly from English into Russian). The best way to find lyric is using of "найти" field (it is in the right bottom side of the web page).
Here are some lyrics as well http://mirpesen.com/ru