I don’t think we’re helping the poor bloke who wrote the OP…
Please to note the “poor bloke” is the one who asked me for clarification.
Hey, MikeS, is this the sort of explanation you were talking about?!
Poor and broke to say the least. Oh, wait, you said “bloke.”
Regardless, it’s straightforward if out of my depth. I’m assuming that e[sup]1[/sup]=(1,0,0), e[sup]2[/sup]=(0,1,0), etc. When speaking of “2-forms”, is this the sort of thing one is speaking of?
So, let me ask this: The language of forms doesn’t put us in the realm of pseudovectors. But does the language of forms tell us what is physically happening, or is it another form of mathematical fiction?
Yeah, that’s more or less it. Gonick’s drawings & explanation are clearer, though. 
Your link to the MathWorld site on differential k-forms is indeed what we’re talking about (where k=2, of course.)
As to whether talking about things in terms of 2-forms is more accurate: maybe slightly, since 2-forms have the advantage that they generalize to higher dimensions while pseudovectors don’t. However, angular momentum vectors and such are easier to visualize, which is why they’re used a lot more often. Beyond that, you’re getting into the issue of whether any physical model can be seen as something other than a mathematical fiction. We certainly seem to be able to describe classical mechanics using vectors, calculus, calculus of variations, etc.; but whether or not, say, velocity really is a vector is an issue for the philsophers.
I’m not sure there’s any difference between the two in this case. As, upon preview, MikeS already said, philosophers might argue about whether a torque vector ‘exists’ in some sense, but physicists don’t care – it’s a mathmatical technique that gives the right answer, so they use it.
It is a slight abstraction, in that a simple torque vector calculation pretends the rotating body is completely rigid and incompressible, the pivot is an idealized dimensionless point, and so forth. In that sense, it doesn’t tell us what’s ‘physically’ happening, but for that matter, all of Newtonian physics is an abstraction, ignoring quantum and relativistic effects.
But it’s still darn useful, and in many, many, many cases makes predictions that are good enough to design bridges, airplanes, race cars, space shuttles, computer hard drives and what have you.
Well, sort of. We’re talking about the general notion of a k-form field, while a differential k-form is a specific type of a k-form field. In fact, differential 1-forms are covector fields.
Everything I’ve been doing is essentially taking place at a single point. If you have a continuous function sending each point of space to the torque 2-form at that point, you have a torque field (like the electric field assigns a vector to each point). So, take the MathWorld page and throw out everything about differentiation and such, as it’s really extraneous to this discussion.