can you let us know if you have localized the Login page resources to Greek, compiled and deployed the dlls to BIN ? This is prerequisite to having localized login page, also if there is no Greek translation then all resources will fallback to English.
As for the Logout/Login control & return URL used in the demo site, can you let me know what MonoX version are you using as there may be an issue with login URL rewrites in older versions ?
"SO I THINK THE ISSUE is with your REWRITE rules or the language bar that fail to add the language to URLs like the one used by the LOGIN button/link"
Can you please let me know if you are using MonoX Language Changer WebPart or your own WebPart ? I was looking at your site and it seems to be adding the language rewrite rule to URL properly ?
"btw, the LOGIN link from the home page forgets to add /lng/el-GR but the logout from the admin page does add it and tries to take you to localized main site login (which fails too though to select the greek in the language bar)"
Can you please point out the login link on your side so we can take a look ?