Could you put up a straight-down picture, showing how far the rod's end protrudes from the wood? I just looked up some strat truss-rod replacement videos, and I'm wondering if this is a Fender neck that would've had a Bullet Truss Rod. If so, It should've extended out a bit - like a bullet - and it doesn't seem, at least from the end-on photo, that there's a bullet shape there.
The non bullet truss rod necks I believedid not have a simple allen wrench adjustment. The only strat I have is a Bullet. If yours is supposed to be the same, it would almost seem the bullet part snapped off at some point. Did you have this guitar as a brand new instrument?
Also I'm wondering if there's a screw-head at the base of the neck.
There's this link I found: http://www.strangeguitarworks.com/fixing-broken-truss-rod/
I don’t think it was intended to have a bullet style truss adjustment. It’s definitely intended to be adjusted from the headstock. There is no adjustment at the heel. It’s a 1999 mim standard strat. I bought it used. The truss rod does seem to adjust when I turn it with a flathead screwdriver. However, from the start it never took an Allen wrench 3/16, 5mm, 1/8th or otherwise.
Good guitars, those MIMs.
The only thing I can suggest is to take it to a repair person. In the closeup I do see the six inner faces of the hex; they do look a little smoothed out though. I don't know for sure, but I'm wondering now if it's metric. Previous owner might have used a standard allen wrench and eventually smoothed out the inner surfaces.
If you can, maybe get a metric allen wrench set and see what happens.