The general rule of thumb is, if it moves, stranded, but if it just lays there, solid.
Jumper wires that bridge rail joints (of which I have, literally, hundreds) will just lay there, and solid wire doesn't spring strands to cause mystery shorts. All of my layout electricals are solid communications wire salvaged from a number of unlikely sources.
Chuck (Modeling Central Japan in September, 1964)
Electrically it is a toss up.
The solid wire is easier to solder and will not have a stray strand to reach up and tangle itself in your trains.
ROAR
The Route of the Broadway Lion The Largest Subway Layout in North Dakota.
Here there be cats. LIONS with CAMERAS
The attached shows single wire and multi-core for various AWGs 24 and larger, indicating that for a nominal AWG that a single wire has more current capability than stranded (if I'm reading this right). I don't know how much of the difference is from wasted space and how much from other electrical technicalities.
http://www.engineeringtoolbox.com/wire-gauges-d_419.html
Paul
Modeling HO with a transition era UP bent
The wire gauge is more important than whether it's solid or stranded. For the use you're asking about, a very small gauge solid conductor such as found in a telephone wire, would suffice.
Remember, you're dealing with very low voltage and low amperage, so small gauge wire will be just fine.
I need to install a couple of jumper wires across some insulated track connecters.
The question is: Which conducts electricity better. SOLID or STRANDED WIRE?
Harold