It sounds like an app you have may be keeping it on, or you may have a stuck button. Check your buttons to make sure there is no dust, food, etc., in them keeping them from moving correctly.
If none of that works, to turn it off, try removing the battery for a few minutes and then put it back in. When you have it back in, see if the device "stays off".
If it doesn't turn back on, on it's own, then start the device in "Safe Mode" to see if the problem persists. If it doesn't happen while in "Safe Mode", it is most likely an app or update that is your problem. I would then suggest uninstalling anything newly installed or recently updated.
If it does persist, even in "Safe Mode" then you may need to do a "Hard Reset" of the device. But I would really save that as a last resort, as it will wipe data.