Oblivion keeps telling me I'm over-encumbered,and thus I can't move about in-game.

How do I fix this so I can get moving again?

You're carrying too many items. Just below your inventory list in the menu you should see a number - for example, 310/300. The first number is how much you're holding, the second is your maximum carry weight. You'll need to drop some items to get that first number below the second.

On PC, hold shift an click to drop an item. I'm not sure about on consoles, I'm afraid.