You cant get them downloaded automatically to your website i dont think.
you could either download them then ftp them all to your server and put links up that way. which is a lot of work. and you will have to do it every time a podcast episode comes out.
but to get an automatically updating link use this plugin (WP RSS Aggregator) and it will link to the most recent podcast episode, if you can find the feed
now how to get that into a player, where the newest episode from each podcast has a press play option may be a little harder. and i dont know how to do that
if what you want is a long list, or a large file conting all episodes, of every podcast and episode like in a itunes library where people can download them, i would suggest the ftp method, just google how to ftp to your web host. Using cpannel or whatever you have, will make you have to do them one by one