For me? Well, I never really experienced the new VR technology.
But to me, the most important part of "presence" is sound. I keep bringing up System Shock 2. The graphics are hilariously awful today, but they were already bad even at the time of release! Mechanical things looked kind of alright, but everything else? Urgh.
And yet you felt like you were there because of the amazing sound design and ambient music. Especially the way they had enemies reveal their nearness through muttering, chittering and various other sounds they would make would draw you in and remind you of the danger that lurked around the next corner.
Seeing your own body like in Arx Fatalis is nice, but not really that important. Speaking of Arx Fatalis, its sound design was amazing, also. Hell, one level's ambient sounds are just like the staircase's ventilation sounds at a place I used to work: For some reason, the air really howls through there. Every time I went there in real life... well... I was reminded of being down in those virtual depths of Arx Fatalis.
Anyway: As I said, sound is incredibly important to me, way more important than the visual aspects of immersion. Which is also why NN succeeds very well to me: The music and/or ambient sounds are extremely well done and keep you on the edge of your seat.
Yet NN is using a cartoony style and isn't even first person! Clearly, I'm not the person in the situation and yet I feel drawn in. Just another demonstration that you don't need to be "in the place" of the avatar nor need to have the VR tricks to feel immersed, to feel present.
I'm sure VR can be of great use for immersion, but when I think back to the games I felt immersed in before its advent, sound design was always at the forefront of what drew me in. Graphics are secondary and even the viewpoint is not as relevant to me, as NN itself demonstrates.
I always wear headphones (cordless) so I can walk around my apartment while listening to music or clips (including your DDs sometimes, matt). I didn't really try NN without headphones, but with them, the sound design works very well, yes. I'm not gonna play in the cold, though.

I forget about my surroundings when I'm really engrossed, so if I play for a long time, I might catch a cold.
Dried blood? But the blood in the game is fresh! It's red and shiny, not brown and dull. But it's interesting that you mention memory association considered how I felt about the sounds in that staircase/Arx Fatalis. A problem with smells - just like with everything else - is that you don't really know what people will associate with them. "Clinical smells" are pretty common around where I work, so they'd probably just remind me of my daily routine.

So it's a bit of a lottery what effect you're going to achieve with smells. But then so is everything else, I suppose, including the auditory and visual methods of trying to affect the player...