Do all the machines have Microsoft Access installed?
Can you search the machines that generate the error to see if you can find the file named OCI.DLL?
Opening an Access Application either requires a full version of Microsoft Access to be installed on the computer, or, in the past, Microsoft had available a distribution package that would distribute the Access Runtime files. I suspect that this file is one of those (though that is just a guess).
Is there any other common factor about the computers that do not work, such as are they running Windows Vista? Sometimes Vista has a problem registering DLLs during an installation (particularly if you are not signed in as an Admin on the computer during installation). If so, then usually unregistering the DLL and reregistering it will solve the problem.