Do players get to heal any strain or wounds between sessions? For example, does your strain or wounds drop back to zero when the next session starts?

A night's rest (in-game) recovers all strain and 1 wound. Beyond medical treatment and stimpacks, the rest is up to the GM.

My games vary dramatically. Usually they only fully heal at the end of an adventure arc, otherwise, as Kasoe states, they only get a night or two to heal. Often they recover nothing between sessions, because they break between encounters (or mid-encounter) depending on my timing.