This is just a guess, but I'm wondering if your artwork from iTunes is stored in an iTunes artwork database; readable by your iPod, but not something that Strawberry can read. I think that if the artwork was embedded in the files, you might be able to see it.
As I recall, you can save artwork a couple of different ways in iTunes. I have always preferred to embed the artwork, where it becomes a part of the metadata, and travels along with the audio file wherever it goes. Takes a bit more storage space, however.
Sorry, I can't test this right now, as I don't have access to an iPod.