What is the best way to moving from SQL Server to Oracle ? in application built using asp.net and c#

Using SQL Server Integration Services (SSIS) is likely your best bet. If you're not familiar with SSIS, the best way to try something out is to use the SQL Server Export Wizard and have it create an SSIS package for you. For example, if you go into SQL Server Management Studio and right-click on your database, then select Tasks->Export Data. From there click next until you get to the "Choose a Destination" step. Select the "Microsoft OLE DB Provider for Oracle" and click Properties to define your database connection. When you click through the wizard, on the Save and Execute page, make sure you check the checkbox labelled "Save SSIS Package", on the next screen specify where to save the SSIS package. Once you finish the Export Wizard, your data will have been exported and you will have an SSIS package that you can use as is, or go in and tweak it to do more specific things. Once you have your SSIS package, you can schedule it by creating a SQL Server Agent Job.

you can use migration tool in oracle to move any database to oracle .

This requires creating a connection in SQL Developer to a live Microsoft SQL Server database. Using JDBC, the Microsoft SQL Server database metadata can be accessed and the Capture Model created

SQL SERVER IS THE BEST ABOUT ASP.NET DEVLOPEMNT

There are many ways, but if you are talking about databases. It will be doing some sort of data migration plan.

In application using asp.net/c#. It would be tedious since a asp.net/C# only deals with a web application not a database.

I think the best compatible DB server is SQL Server especially for ASP.net and C#. Ofcourse Oracle is one of the best DB product no doubt in it. For moving there are lots of syntax and schema  related changes carefully need  to handle as there are lot of syntax and administration differences in Oracle and SQL Server, not so simple, but will not mean impossible as well. Thanks.