Is fine stranded wire ok for main supply line?
I can call it right now. 

I don't see any markings on the wires.   Now, perhaps the wires come out of a multiconductor cable, whose cable sheath has markings that indicate it is one of the NEC/UL rated types of wire legal for mains wiring.  But if not...

Wires without insulation markings are no wires at all. 

You don't even know what you're looking at here.  You don't know what insulation temp column you should be pulling out of for 310.15(B)(16).  You don't know if it's 600V insulation.  We don't know if the insulation will hold up over time, in the environmental conditions, or with the heat of the wires working normally.  For all we know it could be Chinese car battery cable.

Given that it's all 4 colors, there's a fair chance it's cable in sheath, or was shucked from cable in sheath (there go the markings).  This is why you can't shuck NM to get wires for running in conduit.