Finally, I found some old copy of OneNote, installed....and it was updated to the latest Mavericks compatible version "15.4 (141113), © 2014 Microsoft Corporation. All rights reserved."
So, they still have it in Appstore.
But it is unavailable for new users for some reason, only as an update.
Dear Microsoft staff, please give us a link to older version of OneNote compatible with MacOs Mavericks in this conversation. This will close this problem for now.
When Apple will really fix all problems in Yosemite - users will move forward to latest versions. For now just give us older version as a workaround.
Thanks in advance.