My iTunes account shows an incorrect device

The podcasts part of iTunes just manage those you have either subscribed to, or subscribed and unsubscribed but still have episodes. It looks like your issue is related to trying to manually manage these, which will let you add the files to your iPod, but iTunes really doesn't know about the structure behind them.

I would recommend having it manage them for you. In that case, you can also tell it to delete those (or keep those) you want after you listen.

For example, I have a couple of concerts from NPR on my iPod that I keep, but my other daily/weekly podcasts delete after they have been listened too.

I expect the reason you are seeing the difference between iTunes and the iPod is the way you are currently mixing the two methods.

I had the exact same problem several times in the last three years (with an iPhone 3G, an iPhone 4 & an iPod touch).

I always solved it this way :

1. disable music syncing for the device (uncheck everything in the "music" tab)
2. sync the device at least two times
3. enable music syncing
4. sync again

I usually divide steps 3 & 4 in smaller steps. I begin by syncing a few artists to check everything is fine before syncing all the music I want on my device.

I hope this will work for you.