Is labor supply a real or nominal variable? Neither; labor supply is a relationship linking the desired supply of labor hours to real wages and income.

Is labor demand a real or nominal variable? Well, labor demand is the real MPL, which is a real variable, but labor demand is also a function linking desired labor hours demanded to the real wage, output, and the markup.

Putting my Micro 1 hat on, I'd say it's a real variable. Why? Labor supply/demand follows from FOC of the representative agent. The rep agent responds to relative prices. Money is the "M" word in micro, so we don't have nominal variables.

Aggregate demand is a relationship linking the price level (or inflation rate) to output (or output growth, or the output gap) and possibly other factors.

Which (as you pointed out to me awhile ago) doesn't follow from FOCs. It's just a relationship on P-Y space, and something you called "model dependent". I think it's a bit incoherent. Still, I figured I'd talk about it because others do. As I wrote to urnbabyurn, the model in my head is the Quantity Theory, but I'm just mapping it to P-Y space and saying the LHS is AD and RHS is AS. Assumptions about non-neutrality of money makes a vertical or upward sloping (or even horizontal) AS curve.

Since I'm a product of a Freshwater macro program, I admittedly don't know IS-LM well enough to comment on AD being a combination of that. I recall my Jones textbook deriving IS from AD (Chris I. Jones, Standford guy, if you were curious) but not much after that. IS-MP is my short run model, as I've said before.

Quick question though - AD predated household optimization and Taylor rules (well, the concept of household optimization in macro, anyway). Are you sure you're not just trying to hold onto AD here by justifying it with newer techniques?

House, Sumner and Rowe were in the back of my head when I wrote the above comment. Those are cool blog posts, to say the least.