First ensure all of the keys are still responsive to determine whether or not the keyboard can be salvaged at all. Depending on the brand, replacement keyboards can be bought off of ebay for anywhere from $15-$60, so it may be worth it to buy a new one then try to clean the pee'd on one.
Next, you need to remove the keyboard so you can take a look underneath there and see whats going on. Again, depending on the brand this is done different ways. The manual for the laptop should show where the screws are for it, but basically, you unscrew it and the keyboard should lift up and forward away from the screen. Underneath you will be able to see the internal components. Make sure there are no stains anywhere or standing urine. DO NOT use any chemicals to clean this with! Use only a soft cotton towel or rag with a little water to try and lift any stains away. You could also use a toothbrush to lightly scrub on the METAL cover parts, never on any internal components. That should help with the smell a little, next lets look at the keyboard itself.
I would start by using a can of compressed air or contact cleaner to spray through all of the keys out with. The keyboard can be detached from th rest of the computer by removing the thin belt looking cable. It should be attached by two little connectors on the laptop that you can squeeze or pull apart to release it.
Next gently start removing the keys from the keyboard (make sure you make a chart of were they go or get one online later!) This way you can see if there are any urine stains inderneath the keys that would be the culprit of the smell. Again use a damp cloth to rub any stains you see away.
Put it back together and see if the smell is any better. As for the dvd drive, im not sure. That would need to be answered by another member.