I would in this case trust the error. I bet you an organic fig that it's exactly as it says.
Does your SP return rows? If not, that is the problem. Otherwise, it's probably a permissions problem.
Try a simpler query: SELECT * FROM OPENQUERY(LinkedServer, 'SELECT * FROM SomeTable WHERE rownum <= 5') X
Does that work? I can't remember the rownum syntax, but basically you should try a simple select of a few rows.
If you validate the linked server by selecting a few rows, then you're entirely in Oracle land (or SQL Server linked server permission/login setup land) for any other problems you get.