Hi,
If your users have Read access they will still be able to Open the file, do a Save As or do a copy/paste of the content. But they will not be able to upload changes to the SharePoint site.
You have to implement "Information Rights Management". I don't know much about it (Cost, License etc).
You can read more on this topic:
http://office.microsoft.com/en-us/sharepoint-server-help/apply-information-rights-management-to-a-list-or-library-HA010154148.aspx
Hope this will help
Cheers, Hemendra-MCTS "Yesterday is just a memory,Tomorrow we may never see"