Looks like your whole system is very "American". First you should make sure, that you can use cyrillic characters in linux applications. You may have to install some locale stuff in linux.
If you want to use e.g. Russian letters with a specific wine application, you'd run it like this:
LANG="ru_RU.UTF-8" wine yourapp.exe
or simpler
LANG="ru_RU" wine yourapp.exe
where the string "yourapp.exe" is to be replaced with the actual name of the .exe. In most cases it may not be necessary to enforce UTF-8.
In some cases, you may want to enforce russian date formats, currency symbols etc, in this case you'd issue a command like
LC_ALL="ru_RU.UTF-8" wine yourapp.exe
If you want Ukrainian, the commands would be
LANG="uk_UA.UTF-8" wine yourapp.exe
LC_ALL="uk_UA.UTF-8" wine yourapp.exe
I don't know a thing about a Mac, so I don't know how/if things are done a little differently. There is a separate MacOS subforum on Winehq Wine Help main forums page. It is intended for Mac users running Wine. You might be better served by posting there: viewforum.php?f=9