I don't know if you've tried it yet, but it may very well be the font you are using, not all fonts have all the unicode supprt for all languages.
I use arial, as well as a few others I talk to on IRC, and some use Times New Roman, both of these people can read what I type, in any language, just fine. Squares do not appear for anything we've done so far.
Japanese, russian, and arabic have all been extensivly "abused" in some convos, all worked and showed properly.
The only time I ever got squares were when I used some other font that didn't have those characters in the typeset, such as Wellsey, which doesn't even support the ` character.
As for the font support that I have enabled in Regional and Language Options in the windows control panel, they are only for asian languages, not russian or even arabic for that matter, yet arial can display and encode these characters in unicode properly.
As the old mirc, where you had to select, manually, what script you wanted the font to use in order to read such languages as japanese, or russian, that is now done automatically, so long as the fontset that you are using supports it.
I know that was a little redundant, but just trying to prove a point, it could very well be your font choice, and not mIRC itself :P
If you want to look at other fonts that could support the character sets you wish to use, make extensive use of the character map in Start -> programs -> accessories -> system tools I checked all of my nearly 1800 fonts for specific characters (cuz as a TS I dislike using arial at all costs) but still found arial and times to be the best solution since they support the most characters.
Also, using the IME for each language really helps, although inputing the characters from character map is doable, just time consuming, to say the least. I've never been able to test unicode based nicks since I only use Rizon, and they don't support unicode nicks or topics.http://img97.imageshack.us/my.php?image=ircmessages1vj.jpg
<-- these are some of the settings I have, if it would help (yes, sjis/jis conversion is an evil thing)
Edit: As for why the server doesn't handle your unicode, it could be either the way that unicode is getting encoded, or the way that the server reads the characters... We have found, through accident in #help (with mode +c for blocking colors) that some japanese characters do not show up since they contain color codes in them, with how the ircd reads the characters, and as such the msg can't be seen on the channel.
Another thing that can affect how your unicode is displayed, is the unicode for non-unicode programs setting that you have in the RaLO area in windows config. We experienced that, when someone has japanese unicode as their base local, and I had english unicode as my base locale, that i couldn't read the japanese that he wrote to the screen, or vice versa, that is, however, a mIRC bug in not reading the character set that you have set in native windows.