After variuous tests and configuration changes I found out the following:
My old system was an Ubuntu 12.04 with samba 3.6. OMV is Debian wheezy (also with samba 3.6), but now when any share is accessed (even opening "Computer" and showing the network drives is enough), samba writes to disk. The old server didn't do so (I don't kno why). The task that woke my disks or didn't let them go to sleep was my monitoring server, that checked the shares.
Myabe I find out, what the difference between the systems is.