"Narcotic" means numbing, and that's an accurate description IMO. Reports of euphoria are exaggerated. It feels good if you are feeling pain or malaise and it takes the pain or malaise away. Otherwise it doesn't feel like much.
Just to be clear, for anyone else reading this, that's true in the etymological sense. But from a biological or pharmaceutical standpoint, 'narcotic' has a pretty narrower meaning, referring to a specific class of drugs (which tend to produce numbing effects, but not everything with numbing effects is a narcotic).
To make matters more confusing, law enforcement, on the other hand, uses 'narcotic' as synonymous with 'any illegal drug', whether or not it actually is a narcotic (in the biological sense) or has a narcotic effect (in the literal sense that you are referring to).
For example, the 'narcotics unit' will deal with cocaine, which is used as a topical anesthetic for numbing[0], but cocaine is very much not a narcotic from a medical standpoint.
[0] in theory, you could use cocaine for a root canal, but you're more likely to get Novocaine instead.
No, they aren't. It depends a lot on the person, the specific narcotic, and the quantity taken. Some (most in my experience) people feel intense euphoria, others don't.
My only experience with numbing is the dental anesthetic they use in your mouth, which I don't recall producing much sensations but it does noticeably take sensation away.
Those aren't narcotics (most likely). It was probably Novocaine or Lidocaine. Those drugs end in -caine because they're all part of the same family as cocaine, which is not actually a narcotic (but does have euphoric effects at sufficient dosing levels!).
Topical use of any of those drugs, however, will likely not produce euphoria.
For the benzodiazepine class of drugs it's a little less clear cut - people who take them recreationally may well be alleviating stress or anxiety and finding that pleasurable. Opiates.... nah.
I thought that I felt euphoria the first time I took codeine (but I honestly wasn't sure). I have taken codeine since and was never able to replicate that euphoria.
IME with opioids, there will be times when they feel good (or seem to), but those good feelings are frustratingly hard to replicate. I've taken a skeptical look back at all my use and concluded that the drugs simply don't have the power to cause euphoria all by themselves. They can be sort of like a social lubricant, and they can be reliably good when I feel like complete shit. But I never figured out a way to conjure euphoria on command using just opioids.
I'll throw it right back at you - your own personal experiences are worth about as much as mine when it comes to medical evidence, not a lot.
[1] http://www.rxlist.com/oxycontin-drug/side-effects-interactio...
One could easily resolve the question of whether opioids cause euphoria by doing a double-blind clinical study. I would love to do that study, in fact.
[1] http://www.rxlist.com/oxycontin-drug/side-effects-interactio...
Or maybe you're right: they just take away pain. But it turns out a lot of us have existential pain so it works all the time.