The machine where Crystal Reports is running will need an Oracle client installed. There are potentially three different machines involved here-- your local desktop, a middle tier server where Crystal Reports is running, and a database server. Whichever machine(s) connect to the Oracle database would need the Oracle client installed.
I expect that the error message you are getting is telling you that the Microsoft ODBC driver for Oracle requires that the 7.3 or later version of the Oracle client is installed on the machine that is attempting to connect to the database. That is expected if the Oracle client has not been installed-- Microsoft ships a driver that works on top of the Oracle client, not a driver that can directly communicate with the database.
If the machine that wants to connect to the Oracle database does not have an Oracle client installed, you would need to install a version of the Oracle client. You can download this from OTN from the same place that the database can be downloaded-- if you are installing on Windows, there is a separate client-only download on the same page where the database can be downloaded, on other operating systems, you generally need to download the database installer and do a client-only install. The client-only install for Windows is still a few hundred MB depending on the version of the client you get. If that footprint is too large, you can use the Instant Client instead, but that requires a bit more work to install-- it is more commonly used when you want to ship a very small Oracle client with an application you are developing, so it assumes that you'll be writing the installer and registering the appropriate DLLs.
Justin