Stranded is for vehicle use because it is flexible enough to avoid fatigue breakage when moved and vibrated. Not the case in house wiring. There is an effect, but at high frequencies, not enough to even consider at 60 Hz in AC house wires. Jim
The following is from Argon National Laboratory:
DC current will use the wire's whole cross-section evenly.
Imagine a single solid wire divided by invisibly-thin barriers into parallel strands of equal thickness and shape. Only at the ends are they joined together, metal-to-metal. In this picture, each strand has equal resistance, and equal voltage from end-to-end, so the current in each is equal.
Only AC has a preference for a particular depth. It prefers to be shallow, staying towards the outside. This is a consequence of changing magnetic fields caused by the changing current.
If it is DC, it is not changing, so the magnetic field is steady, and has no effect on the DC current density. DC current only cares about resistance, not inductance or magnetism.
Weird but moot minor point: The steady field around a wire with DC current may cause a small voltage difference between the outside and the inside. However the difference at one end cancels out the difference at the other.
Due to electromagnetism, parallel currents attract. So if the metal conducts electrons, then they are squeezed inwards, and the interior would be slightly more negative than the outside. Contact at the starting end is made to the wire's outside. So is contact at the finishing end. So an electron going travelling the wire-center route may go up a small potential step at the start, then go down the same amount at the end. These two steps cancel each other out. The end-to-end voltage in the wire interior is the same as the wire exterior, so the current densities are the same too.
Nobody even thinks about those last two paragraphs. They do not need to. Except maybe physicists doing plasma hi-power sparks with Z-pinch. Z-pinch is when the glow of the current in the ionized gas spontaneously squeezes itself into a very intense sharp narrow strand, even though it started out wide and diffuse. It only does that if the current is very high, and because a gas can be compressed. In a solid metal the mobile electrons (charge -1) are forced to keep a constant density by the need to keep charge neutrality with the hard-packed metal-ions (charge +1) they wander amidst.