Can I save bodies?
Bodies are removed when the "cell" (in this case, the house's interior) resets. The trick, then, is to prevent it from resetting by visiting it at least once every ten in-game days (some reports on cell resets go as high as thirty days, but as you're trying to avoid a reset, you ought to play it safe).
If this house is your primary base of operations, that isn't likely to be an issue for you, but be careful when waiting for shop inventory resets and the like; you don't want to stay away for too long!