I've solved the problem and want to write down the sollution here too. Maybe its helpfull for somebody.
I call a stored procedure with about 13 parameters from my asp page. I use one in/out parameter, 9 in parameters and 3 out parameters. And the out parameters are the problem. It seems that only 2 out parameters of the type VARCHAR2 or VARIANT are supported. Using more than 2 out parameters of the type varchar2 or variant causes the error ORA-01023: Cursor context not found (Invalid cursor number)
Source: Microsoft OLE DB Provider for Oracle number: -2147467259.
Strangely it only does that on one server.
Now I concatenate two OUT parameters first and later in de code SPLIT them again. This works fine.