dojo and extJS are kind of similar in the way of offering comprehensive layout framework. Having worked with both I find extJS much easier to live with. At the time I worked with it - about 3 years ago - had a really horrible way of defining controls with templates in one directory and code file in another. It was a nuisance because it was hard to troubleshoot any problems with the layout/code interaction.
ExtJS has everything defined in javascript and the layout just works. I find it much better as everything is one place. They both offer same cross-browser wrappers for most of the functionality you need.
jQuery is different kind of beast is better suited for working with HTML that you define(I think). Not sure about layout capabilities - I think you still need to do a fair bit of your own HTML/CSS. The advantage of using jQuery is the terseness of syntax and the fact it's so light and unlikely to mess with other frameworks that you might want to use.
So to summarize between dojo and Ext - its Ext hands down. dojo just sucks. If you want to manipulate your own markup - definitely jQuery.