and please neglect details regarding actual trim of a 2x4 (1.75x3.75 - I think)

Assume the exact same overall dimensions as a 4x4.

The way you choose the bolts and the distance between is also a determinant factor for the composed beam.

If you look at old houses you may see between 2 beams transverse pices of wood which have as goal to fight the sliding.

Thank-you for your answer,

How about if the 2x4's were placed on edge so that the "seam" is vertical - would they have the same strength as a 4x4?

Yes! They would in flexure under gravity load, but not in torsion or horizontal load.

Yes, since considered this position relative to load the W= (b/2)*h^2/6 for each one. Multiplied by 2 it is equal to the W of full section.

no. But the two members must be fastened together, and it does give you the opportunity to greatly increase the stiffness by adding a sheet of plywood in the joint to reduce deflection. 1/2" thick OSB will greatly enhance the bending and buckling resistance (assuming the OSB sheet is normal to the bending load.--i.e. floor joist joint is vertical.) American Plywood Association provides guidelines for calculating loads,etc.