It is possible to method to connect with an online oracle DB from the client PC without setting up oracle around the client ?

You have to download an ADO.NET driver for Oracle. Here is a step by step guide.

You don't have to install all Oracle only the ODBC driver.

Everything is dependent upon the remote server. When the remote server isn't enabling remote use of db then u cannot can get on anyway.Rather u have to build some kind of webservice and deploy that web plan to exactly the same remote server. And call the net service to your application. The net service will behave as a nearby application to db and can return your preferred things, designed in code. If it is permitting remote access then as adviced above are great options.

I really hope, you first got it.