Recently I was washing my wife's Odyssey and I thought to try Comet with a wet blue paper shop towel. It scrubbed off the oxidation pretty well. The next step was a rub down (easy ODT) with NuFinish and buff till dry. They turned out really well.
Now mind you this cleaned up the oxidation on the outside. Most lamps are sealed and can't be maintained. If you have a twist lock type bulb I suppose you could remove the bulb and the whole light "bucket" assembly and blow it out and get whatever is in it out. Taking the assembly out may prove difficult however.
Not going to be able to get to the inside most likely. They sell the refresh kits which I think is basically wet sanding the outside of them and I have seen that turn out pretty well.
generally its just easier to replace but sometimes the options are crazy expensive. if you headlights are sealed then there is at least one trick you can try. You can generally pull the headlights out of the car and stick em in the over at around 170 for a couple of minutes and this will soften the glue holding them togeahter. Sometime you can get them apart after this and clean them, sometimes not.
I used one of the restore kits on mine and my wife's. It was just outside though. Defiantly made a difference. If you feel like being a cheap skate, toothpaste works pretty well also.
Buy replacements (not OEM) off Amazon for $100-150. Plenty of reviews so you know what you're getting. Then you're good for another 10 years with no scrubbing or worrying about it.