A co-user (thanks Matthias) pointed me towards this link
that shows how to activate office 2010 in crossover. Here is the process (copied from the above link:
There are three different registry entries that have to be added:
Use regedit for this task. It is very important that you do not close this the whole time.
"KeyManagementServiceName REG_SZ <Licence server>"
"KeyManagementServicePort REG_SZ <Port of licence server>"
Start MS Office (i.e. Word). Then an additional entry will be automatically created:
Update "regedit" for example by pushing "F5"-key to see this change. Go to
"VLRenewalSchedule REG_BINARY <any value>"
this worked for me