The person who made this is an idiot

/thread

"We have a source of infinite energy" should be enough to tell you something is wrong (unless you want to think of the portals exactly like in the game in which case anything goes because the games physics is made up).
IRL the portals would probably cause a distortion in spacetime as if some virtual replica of all the masses in the universe (rotated and translated the same way the portals are rotated and translated from each other) probably with a speed of light delay moving outward from the portals (or the mid point between them?)
The end effect is that things sitting directly between portals vertically displaced, pointed at each other, and on a planet would be wight-less (and maybe the earth would explode?)

I was going with the spirit of the game physics, as even though what he made was autistic, we're talking about Portal.

In that case it doesn't really matter.
Portals are destroyed as soon as the move so the middle scenario doesn't make sense.
Moving a portal while something is in it instantly teleports the thing (there's only ~ 1 time you can do this by placing a portal on a ceiling panel moved close to the floor and placing another one elsewhere on the floor. Then have chell stand in one and shoot the gun and you will be teleported but that's probably because Chell's body is unbreakable)
The rod would fall forever of course just like everything else in that game.

Is the whole portals concept even consistent in the sense of the resulting space being 3D space with a zero-length wormhole through a fourth dimension connecting two elliptical shapes which can be arbitrarily placed? If it's theoretically consistent, would it make any sense to apply physics (such as gravity) to it, or would it break at least once physics were involved?

Portals don't exist. Problem solved.

I have no clue how gravity works (the equations I've seen require an understanding of tensor geometry)
We do know the portals pass coherent light. (Turret lasers) The don't seem to pass non coherent light (otherwise dark areas near a portal who's partner is well lit would appear well lit) but I think it's reasonable to attribute this to the complexity of making accurate shadows in real time.
They must pass electric/magnetic fields otherwise there would be an interruption in the power supply on the turrets (which almost certainly contains coils and capacitors)
I'm not convinced gravity would be different.

>require an understanding of tensor geometry
Tensor geometry isn't a thing. Tensor calculus is one possible language used to do computations in differential geometry. It is the one most often used by physicists because it is the least abstract.

Springer has a whole book on this titled something like "euclidean worm holes". The spam filter won't let me post a link.

Case A, rod does accelerate downward.
Probably eventually hits the edges of the portals from not being center perfectly.

Case B, rods turns sideways as much as possible.
If "as much as possible" isn't enough, it snaps with a ridiculous amount of force.
Probably along that shitty ass solder.

Case C, rods gets cut along the moved portal's old edge.
The flies out of the new portal (probably at terminal velocity, from falling for so long).