Melee heroes' bashes stack fully, where if two bashes occur at once, the longest stun time from all of the bashes, and each and every seperate bash's damage will work. The damage is reduced by armour type spell resistance (and eliminated by magic immunity), but the stun is not blocked by magic immunity. The damage is counted as a seperate source, and does thus not affect lifesteal, nor is it affected in any way by criticals.

As for ranged heroes, if two bashes occur at once, only the bash time and damage from the last bash skill or item you got will work. The damage is hero type physical damage, that means it's not blockable by magic immunity and it's reduced by armour type hero resistance and armour value. The stun, however, is blockable by magic immunity. The damage is added as your normal damage, but will be skipped if a critical triggers after it (essentially the damage you deal will be BaseDamage*CritMultiplier). If the bash instead triggers after the critical, the damage will be added after the critical strike has multiplied the normal damage. (BaseDamage*CritMultiplier + BashDamage)