I can't write and listen to any talk radio show, though I have to have music on. I've tried listening to The Best Show while I grade papers, but it just annoys and distracts me. Sometimes I'll answer emails with it on (this is why I sometimes disappear from the chat, when I'm in the chat, for the none of you who were wondering), but that's about as advanced as it gets. Does the chat count as multitasking? It does get tangential sometimes.
Usually I'll cook while I listen, unless I have to catch the podcast, in which case it's all about zoning out on a commute. I have certain neurotic podcast rituals - for example, I have to listen to Democracy Now when I leave the house to go to Jersey, This American Life or Seven Second Delay when I'm waiting/checking in for a flight, The Best Show when I'm on a plane, Sinner's Crossroads during my office hours (though actually this is mostly because I share my office and who doesn't like old-timey gospel?). There are a few others but those are the big ones.
