Is the question "Can we use multiple databases in a single ASP.NET application" ?
For most cases, you can
.net Framework has classes and APIs ready for both SQL Server and Oracle (System.Data.SqlClient and Sql.Data.OracleClient
For MySql there's a libray available for download at MySql web site.
But for others you might need to use OLEDB / ODBC.
Most of the database-related classes inherit from the base classes in System.Data.Common
For example, System.Data.SqlClient.SQLConnection and System.Data.OracleClient.OracleConnection inherit from System.Data.Common.DbConnection
Put it simply, you should be able to use the same technique with different data sources.