I believe the MSSQL ADO.NET Providers (drivers) are installed when the .NET runtime is instsalled, but it looks like you're rockin MySql. You're best bet is to use the .NET ADO.NET Provider for MySql (not the ODBC driver), it's called MySql Connecter/.NET. Technically, the ado.net provider still has to reside on the machine that's making the call to the database (i.e. - web server or client workstation) but you don't have to "install" it... you can package it with your app via xcopy or ClickOnce, etc... I believe the ODBC driver you speak of must be installed via installation exe or msi. Also, ODBC is old and slow and you should not use it unless there is a specific requirement to do so. Use this:
http://dev.mysql.com/downloads/connector/net/6.0.html
You will be able to use ado.net just as if it were using MS SQL Server.
This will also work with the entity framework i believe.