I have had this problem in the past too. I"m guessing by "eyes" you mean burners. Most normal stovetops actually come apart, believe it or not -- I discovered this after one of my cats did the very same thing as yours, and I was determined to eradicate the smell. LOL
The drip pans come out and the burners themselves even unplug and come off. If you look, you can see where the coil plugs into the base of the burner. It just unplugs like a regular plug into a wall outlet. I'm not sure whether it would be a good idea to submerge the ENTIRE burner coil unit in water (by which I mean the plug part as well). You could contact an electrician or your stove manufacturer for information on that. But you should be able to submerge the coil itself, while leaving the plug out of the water.
In addition to the burners unplugging from the stove, the stove top itself should also flip up like the hood of a car to allow you to clean inside the stove. Don't be afraid. It's all self-contained. There aren't any exposed wires under the stovetop or anything like that.
Any normal cleaner will get rid of urine that's inside your stove top. Since it's not a porous surface it will come right off. If you have pee actually inside the plug part of the burner coil... I'm not sure what to tell you about that. Try contacting the stove manufacturer. It may not make you feel any better, but any pee you can't get at will eventually "burn off."
Depending on the actual design of your stovetop and drip pans, you may be able to prevent future messes just by buying some cheap metal burner covers from Wal-Mart. If rotten kitty does it again, they should keep the pee from getting into the burners.
Some cats continue to do things like this. In my experience, when I've waited too long to have my male cats neutered and they've already matured and started scent-marking, this is something they will continue to do sporadically throughout their lives. (The cats I've had neutered BEFORE they were mature enough to start spraying have NEVER had any problems with inappropriate scent-marking.) Also if he's REALLY new to you, this may be something he'll outgrow once he fully realizes that it's HIS house and he doesn't need to mark territory.
If peeing in inappropriate places is a new behavior for your kitty, you may want to have him checked out by your vet, perhaps have a urinalysis done. Such behavior is a common way for your cat to alert you to a health problem he's having.
Good luck with the clean-up, and I hope your kitty is healthy!