This info comes from the Codeweavers page for MS Office 2010, but it didn't come up when I searched for it...
To activate MS Office 2010, running in Crossover Linux, against a KMS:
Start the "Manage Bottle" dialog from your CX installation, select your Office 2010 bottle, click on Run Command and type "regedit".
Navigate to HKEYLOCALMACHINE\Software\Microsoft\OfficeSoftwareProtectionPlatform
Create the following 2 keys via Edit -> New -> Key: String Value:
Keep regedit open and start any MS Office application (i.e. Word).
Go to HKEY_USERS\S-1-5-20\Software\Microsoft\OfficeSoftwareProtectionPlatform
Insert the following key via Edit -> New -> Key: Binary Value
Restart the office application; it should now be activated. You can check that by going to File -> Help.