It does not matter whether your instruments are solid wood, or cheap doorskin plywood... IF it gets dry enough wherever it is that you live, such that you get static shocks when you walk across a carpet sock-footed; then YES you need the house/room humidified. Not just for the instrument but for you! Bowls of water set out with a sponge in them will help -- as long as they are kept replenished. Damp towel(s) over heater vents will help too.
Where I live in South Florida, however, that is never an issue.
Those miniscule (and I do mean miniscule) increases in string diameter will NEVER harm your instrument! You can re-string it as a baritone using much heavier strings and it won't hurt anything.