Looking for strategic advice on how to deal with these buggers.
The following weapons will take out a Mini-Sentry in one (direct) hit:
If you have one of these weapons, it should be no trouble to pop out from behind cover and peg the Mini-Sentry before it does too much damage to you. Shooting them from out of range is better, since buildings take consistent damage regardless of distance, so if that's possible it is preferred.
Aside from those weapons, other Rocket Launchers aside from the Cow Mangler will deal 90 damage on a direct hit, leaving the Mini-Sentry with 10 HP so any splash should finish it. Shotguns, scatterguns, and miniguns can deal with Mini-Sentries pretty fast at close range, but it may be difficult to get into such range due to the knockback, and the small target makes bullet spread very significant outside of point-blank (Scouts that beat the knockback might die anyway if too many bullets miss). While inefficient, spraying pistol fire (or anything, really) in the Mini-Sentry's direction from out of its range will eventually wear it down (as it cannot be repaired, any damage is good damage). Sapping them is of course effective.