In the web.config add this
<add name="ORAConnectionString" connectionString="Data Source=10.XXX.XXX.XXX:1521/SOE;User ID=XXXX;Password=XXXX;" providerName="System.Data.OracleClient"/>
This assumes that you have the client installed -- it also allows you to connect with using the TNSNAMES
I wouldn't suggest using system.data.oracleclient. That was deprecated awhile ago.
You should use one of the .Net providers from Oracle instead.