If an interior polish / quick detailer spray wont clean up your steering wheel, and replacing it is out of the question, you could look in to adding a steering wheel cover.
There are the elastic style steering wheel covers which just slip over the wheel. and there are the leather wrap ones, which you first cover with a (faux or real) leather wrap, and then wind the included twine around it.
As for the center Toyota logo badge, you can remove the old one by heating up the glue under it. Then replace it with one ordered from Toyota, or eBay.