A Portal refers to a page that allows users to customize their own homepage by dragging and dropping widgets onto the page. This approach gives users complete control over what content they see on their page, where they want to see it, and how they want to interact with it.
A widget is a discrete piece on a Web page that performs a particular function and comes with its own UI and set of features. Examples of widgets include a to-do-list, an address book, a contact list, an RSS feed, or even a clock, calendar, playlist, stock ticker, weather report, traffic report, dictionary, game, or almost anything you can imagine that can be packaged up and dropped on a Web page. In a corporate environment, widgets can connect to internal systems, such as an Expense Tracker widget that interacts directly with the internal Accounting System. If you are familiar with Sharepoint Portal, then you already know about Widgets. They are called Web parts in Sharepoint's term and also in ASP.NET 2.0.
Portals are powerful RSS aggregation platform. You can put as many RSS widgets as you like on your page and get fresh content delivered to you as soon as it is published. Some Portal like Pageflakes archives RSS for a long time and thus you can go back in time and read older posts, save posts, and forward interesting articles to your friends.
An Ajax-powered portal is specifically a portal that uses Ajax technologies to create richer experiences for its users. It is one step ahead of previous generation portals like My Yahoo or MSN.com, because it gives you state-of-the-art UI that behaves more like a Windows client application -- with widgets, animations, popups, client side data grids, and other effects not usually found on a non-Ajax Web portal.