Power (strength) should have a role in determining melee damage, the range of equipment a soldier can use, the impact of armour encumberance, spread/recoil management of certain weapons, and the maximum distance of thrown objects. Increasing it would result from the participation of a soldier in activities immediately related to the concepts influenced by this attribute (throwing objects, moving while encumbered, etc...).
That said, health experience consequently, should stem from a combination of speed and power experience, and should be penalized for injuries suffered (penalties starting out small, but getting exponentially larger as injuries compound). If such injury is severe (50% or more of max health lost), all health experience for that mission is lost, and permanent health loss occurs, to an extent based on both the severity of the trooper's injuries, and the trooper's pre-reduction maximum health (people who are initially healthy to begin with tend to recover from lasting injury much better than those who are not).
Mind experience should also be derived from use of support equipment and gear (e.g. Medikit), and have an influence on the extent of their success and TU costs (in so far as I understand it as both an amalgum of both strength of will and intelligence). Mind experience should also be gained from successfully resisting panic or using/withstanding psionic attacks (when they are implimented).
Misses with weapons should be rewarded, initially granting smaller bonuses at lower experience levels relative to hits, and larger ones at higher experience levels relative to misses. This is because you tend to learn more from success as an inexperienced individual than you do as an expert. Success for the greenhorn, whether by skill or chance, often contains a wealth of lessons and common denominators that when throughly analyzed, can result in a quantum leap in understanding, as opposed to the much slower, iterative advance that comes through learning through failure, which tends to offer fewer valuable insights. The pro in the meanwhile, has a fairly intimate understanding of proper technique and approaches. He learns more through failure, because it typically highlights weaknesses in his robust methodology which can be acted upon to further improve it. Success by contrast teaches him little, emphasizing instead the value of what he already knows to be of worth.