So here is the problem - we have a russian version of our website and we've decided to make use of our URLs. In order for them to work to our benefit we have to enrich them with Russian keywords, what we don't know is whether we should transliterate russian characters into Latin ones or just use them as is.
The later results in ugly looking URLs when copied from the address bar:
Personally I wouldn't put non-ASCII characters into an URL. As you've seen, the potential results are simply too messy.
Transliterating is not likely to work. It's a viable option if your site uses one of the (very) short list of languages that are regularly written in both Roman and non-Roman script and that have a single standardized transliteration system. Otherwise your URLs are more likely to show up in searches for some non-Russian word that happens to be the same phonetically.
Page titles on the other hand are useful. Just remember to put the meta charset declaration before the <title> tag.
Have you checked what other Russian sites do (not only on Google but on Yandex too). I would choose a selection of local queries where the result would be Russian sites aimed at Russians and check how they handle it and what is more prevalent.