I think that's pretty normal. A quick poll of the other three people in the room reveals that none of us experience an 'inner voice'. It's more like a stream of associations, some of which might involve vocalised words, others might involve images, sounds, or recalled emotions. Sometimes the associations are sequential, sometimes they are parallel. Steven Pinker refers to this as 'mentalese'.
Edit: also, this: http://xkcd.com/610/
Of course, this could potentially be less typical than I usually assume. I've noticed writing notes to work through my thoughts is ridiculously limiting, because my train of thought goes 2-10x faster than I can write or draw. I've always wondered about that, because it seems to be a popular method for brainstorming.
I have both a strong inner voice (which is not perceived as a "voice of God" but more like speaking without uttering) and a weaker mind's eye, and a mind's ear (I can listen to songs I know with what seems like perfect reproduction, though it's definitely perceived as internal rather than external in origin). I also have peripheral awareness of other inputs into my thought process. I sometimes have ideas present themselves all at once, as though several words are silently present in the back of my consciousness, or as abstract notions, or as connections between components in a system. In the end, though, my thoughts don't feel "official" until I've serialized them into a linguistic stream, or at least given the mental images a good "look". This makes reading slower, as I have to read the words at roughly a spoken pace, but I still experience vivid imagery, and occasionally wonder how I ended up back in my house when I take a break from a really good book ;-).
For me, writing is definitely slower than thought. When I first attack a problem, dozens of concepts, edge cases, and other considerations will "come at me" from all corners of my mind. For me writing my ideas down isn't about brainstorming, but calming the storm.
I'm curious what my mental model of my mental model looks like in terms of neuronal connections. I'm also curious how many people are curious about their own thought processes. This discussion thread on HN has been very interesting, as we've seen comments from many different types of minds, all capable of expressing in verbal form their different ways of perceiving thought.
It gets tiring. Recently I've taken up drawing; when I draw my head is finally quiet.
I'm pretty much the same way. I'm not sure I'd say I exactly "hear" my "inner voice" but my thinking is definitely dominated by "spoken word" stuff.
Of course, I also talk to myself out loud sometimes, when working on a hard problem. Not sure how "normal" that is, but I can't say I really care a whole lot either.
Or you can turn it all off and focus entirely on your senses themselves. This can be interesting when, for example, you imagine something in contact with your body as a part of yourself. Do that to your car, for example, then you start to pay more attention to exactly how your wheels grip the road and you have a more intuitive feel for where every part of the car is in relation to you.
Amusingly, as someone with an inner voice, I used to think the same thing about the mind's eye. I couldn't visualise anything with it, and I asked someone else and he couldn't do it either, so I decided probably no one could do it.
Since then I've realised that the people who talk about visualising things are... y'know, actually visualising things. It turns out that some people do and some people don't.
I think it's fascinating how we all have basically the same brain hardware but can end up with remarkably different inner experiences.
Like you suggested, I also think in spoken words when I'm questioning myself, playing devil's advocate. "Why does that matter?" "Is such and such really the case? Prove it." "You're ignoring some really important factor over here."
I find thinking AND trying to record stuff frustrating. If I'm dictating to a recorder I'll always speak in fragments of sentences, or talk ridiculously fast if I'm on a train of thought, because I can feel the next three or four links & associations coming, and I'm scared of losing them while I finish the one I'm currently talking about. Of course, being scared of losing them pretty much guarantees that you do.
Regarding the "inner voice", I find it's always self-directed. I can keep thinking, but choose to talk or not talk in my head. I suppose, if ever you get words in your head that aren't self-directed, pay very close attention.