RadControls for ASP.NET AJAX can be used in SharePoint Farm solutions. There are no ASP.NET AJAX controls, which can work properly in Sandboxed and Client object model solutions. Unfortunately Sandbox and Client object model are the only solution types allowed in SharePoint online. So the answer to your question is that you can not use Telerik's AJAX controls in solutions for SharePoint online.
However you can use other Telerik's product. This is the Kendo suite, which contains only client side controls. Check the following site for more info: http://www.kendoui.com/. There are a lot of resuorces of how to use the Kendo UI controls including an Introduction To Kendo UI PluralSight course.
the Telerik team
Learn how the Telerik controls can be integrated in SharePoint 2007/2010 from this resource
. To watch them in action, explore our online SharePoint 2010