From the Russian computer-animated comedy show Мульт Личности, caricatures of Putin and Medvedev sing "Новогодние Частушки" -- and this version has subtitles in Russian, so that non-native speakers can understand the words better. Whatever one agrees with the political humor or not, as a learner of Russian I found it to be quite an enjoyable translation exercise:
Новогодние Частушки
P.S. Technically speaking, of course, частушки are not "limericks" in their concrete form -- a chastushka is a four-line verse in trochaic tetrameter (TA-ta, TA-ta, TA-ta, TA-ta), while a limerick has five lines and is based on the anapestic foot (ta-ta-TA, ta-ta-TA, ta-ta-TA). But one can made a good argument that they are very much the same in spirit, although not in structure.