We have the Oracle 10g client on users PCs to use the 10g ODBC to connect to a 10g (10.2.0.4.0) database. Now we are upgrading to an Oracle 11g database, 184.108.40.206.0. Is it possible to install the 11g ODBC drivers onto the users PCs without installing the full Oracle 11g client?
Unless you want to go down the Instant Client path, no.
However, there is probably no need to do anything to the clients. Any version of the 10g client should have no difficulty communicating with an 11.2 database. There is likely no need to upgrade the existing clients when the database is upgraded. The only exception would be if your application is trying to use some 11.2 feature that requires changes on the client to support-- those are pretty rare in this instance.
You may want to roll out 11.2 clients on new machines as they come online but that's likely about all that you need to do.