Velira means “great worker,” derived from the elements velikiy rabochiy. I loved this name so much on first sight that I had to use it for one of my characters, born October 1934 in Kyiv, living in Isfahan, Iran for a few years, and then finally coming to America in 1940. It’s just such a cute name, and could easily pass as a regular name since it already looks so Slavic. The basic nickname would be Lira, with superdiminutives including Lirochka, Liroshechka, and Liroshenka.
Vilorik means “Vladimir Ilyich Lenin is the liberator of workmen and peasants,” derived from the phrase Vladimir Ilyich Lenin osvoboditel rabotniki i krestyan. Ironically, given how strongly atheist the USSR was, the word for “peasant” ultimately derives from the word krest, which means “cross.” This root forms the basis of many words related to church, baptism, and Christianity.
Sources consulted:
http://panzercentral.com/forum/viewtopic.php?f=96&t=36301 (penultimate post)
http://www.namenerds.com/uucn/listofweek/soviet.html
http://horo.mail.ru/namesecret/
http://www.devichnik.ru/9810/imia.html (male)