Is it possible give my xbox 360 to my son?

You can just make him his own account and sign it in on the Xbox 360. I'd also suggest making him a

child's account depending on his age, this way thing's don't get accidently purchased.

If he lives in the same house as you do , you can even let him play on your account.

It would be better to create his own account. Especially if he is younger and parental controls need to be put in place. Plus it would be better for his progress to be tied to his own account to avoid problems in the future.

Yes. And it is just as simple as creating a new account for him.

Your son can absolutely have your old 360. You can choose to return your XBox360 to its original state by deleting any content you previously downloaded (i.e. games, apps, profiles). If your son in younger and you feel parental settings are a must, you can
still have them applied to your 360 when you give it to him.

I would suggest having your son create his own Xbox account (if he is of age), this will allow him to create his own save files on games he plays and it will not interfere with any you have created under your profile.

You can still have your own profile logged into the 360 so you don't lose your content. This would be separate from your son's account so the two won't mesh, thus leading to confusion on whose save file is whose.

Yes it's possible.

If he lives in the same house as you do , you can even let him play on your account.