Eudora doesn't have a provision for user-defined MIME charsets, it forces iso-8859-1 for all messages with 8-bit chars.
You can use KOI8 Plug-in for Eudora (free). This plugin can automatically put KOI8-R charset into the message header.
Don't forget to turn off the Quoted-Printable option in Eudora setup.
See also Win3 Eudora Fix.
P.S. I wouldn't recommend Eudora due to its Russian-hostile nature, use The Bat! or Microsoft Outlook Express instead, it provides all Eudora features plus a good Russian (KOI8-R) support.