OLEDB and ODBC are two different database API's. ODBC is an older standard and is actually not specific to windows - you can get Unix-based ODBC libraries. OLEDB is a COM-based API for database connections.
There is a driver for wrapping ODBC with an OLEDB front-end if the database you are using does not come with a native OLEDB driver. IIRC DB2/400 and Sybase OLEDB drivers (for example) use this method.
The ODBC administrator in Windows is only concerned with ODBC drivers. Both ODBC and OLEDB can use connection strings, which have a slightly different format. You can tell from the connection string - www.connectionstrings.com has samples of connection strings for many different database drivers.
Edit: Oracle has a driver technology for every day of the week.
Oracle have a native OLEDB
driver called 'Oracle provider
for OLEDB' or some such. If you're
using ADO (non-.Net, which sits over
OLEDB) this would be the preferred
driver.
They also have an ODBC driver
that would be (for example) useful for
extracting from an Oracle database
into MS-Access or with an application or system that does not support OLEDB. For example, older Delphi/Oracle or Powerbuilder/Oracle apps will probably use this driver.
Oracle also has an
Oracle-specific interface called
OCI. This is the fastest
interface if you're writing in C and
will also work on non-windows
plaforms but ties your application
to Oracle. Dynamic language bindings such as cx_Oracle for Python tend to be wrappers around OCI.
If you're using .Net you probably
want ODP.Net rather than
using the .Net provide for OLEDB. This is the
standard .Net interface library
provided by Oracle.
There are several JDBC drivers for
Oracle. There is a type-2 driver
which is a wrapper for OCI and a
type-4 driver which is written
natively in Java and communicates
directly over the network to the
server. If you're using Java the type-4 driver is probably the best for most applications (you don't have to install a full Oracle client) unless you have a particular reason to need the type-2 driver.