You can do this with the ResourceReader class.
But there's no good reason to give up on the convenience and type-safety of My.Resources. Simply add a class library project to your solution, call it (say) MyRes. Click the Show All Files button in the Solution Explorer window toolbar. Expand My Project and double-click Resources.resx. On the toolbar, change the Access Modifier property to "Public". Add resources like you normally do. Add the project reference, you can now simply access the resources in this separate dll in your code. For example:
Me.BackgroundImage = MyRes.My.Resources.animation