I've done some worse than that, but yours is pretty bad. first you need to get the existing finish off. Sanding is NOT the way to do this. You will end up removing far more wood than finish
. I have used aircraft paint stripper in a rattle can. If the finish is an epoxy, all this will do is soften it. Time for steel wool and more stripper. When all the finish is off, wash it with soap and water. liquid Dawn works well and will show where finish remains (blotchy). It will also raise the grain in the wood, and clean up grease. With all finish off, let it air dry about a week. Then experiment with strong twine to see how much you can close the splits. If twine won't do it, go to clothes line.
When you find out how much you can close the gaps, buy some clear Devcon Epoxy. NOT the 5 minute hardening type
. You will need more time than that
. Mix epoxy and poke into the cracks with a toothpick. You do not need to do the whole wheel at once
. Wrap tightly with twine or clothesline past the glued area and allow to completely harden. Then get as much of the twine / clothesline off as possible. It will be glued to the wheel
. Continue until all the cracks are repaired, and the wheel is a fuzzy mess
. Attack the stuck on wrap fragments with a dull knife like scraper. Remove fuzz and dried epoxy, not wood! When you have as much off as possible, now is the time for 220/ 400/ 600 wet and dri sandpaper, CAREFULLY, by hand, removing remaining epoxy , not the softer wood
. When satisfied, moisten with a sponge, allow to dry, raising wood whiskers. With 600 paper or 0000 steel wool, polish off the whiskers. I prefer a 2 part marine epoxy clear finish, sprayed on. Once dry, steel wool again, and apply a second coat. (You did mask of everything you did not want coated forever with epoxy, right?
If you did all this correctly, you will have a wheel that looks better than new. If you are not up for this job, there are several wood steering wheel repair sources listed in Hemmings Motor News. Still cheaper than a new wheel. Have fun