I would be very suprised if there was any noticable difference in voltage drop between stranded and solid core wire, presuming of course that the sizes were the same.

#12 AWG is #12 regardless of solid or stranded construction.

For a permanently installed 12 volt lighting circuit I would use standard house wiring cable, but a least one size larger than useual to reduce voltage drop.
Remember that a loss of one volt is trivial at 120 volts, but is nearly 8% of a 12 volt supply.

It is unlikely that vehicle wire will comply with the NEC for domestic installation.