My two and a half pence and I may be wrong
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To me over strength though valuable is not the most effective way of maximising your unit effectiveness, what over strength does do is have two effects, it increases the number of potential shots/dice rolls in any particular combat and also increases the time, with losses, it is viable to use a unit within a specific scenario. The shots part is simple (well dependant on rate of fire) but say a basic infantry unit of strength 10 gets 10 shots in a combat each over strength adds a shot Str 11 gets 11, 12 gets 12 etc. Obviously those extra shots give extra kill chances so over a 20+ turn scenario give you more chance to kill off more AI units. The time in use issue comes from the fact that with combat mechanics weak units suffer against stronger ones(those damned shots) and that in terms of building a prestige cushion you really don't want to be reinforcing with a scenario, only at the deployment stage when its cheaper. I personally tend to over-strength units to 11 as that point at deployment costs the same as reinforcing from 9 to 10 in scenario would. I do it because when a unit is at str7 or below I will try to avoid using it in combat if possible, starting at 11 is less likely that their str will drop that low and that I will be forced into reinforcing in scenario (obviously soft cap rules may have an impact on this).
There are however other things than pure over-strength to consider, so lets look at them, where to start.
SE units. Well as free deployments each scenario they are going to be deployed a lot they are also a little cheaper to reinforce/replace casualties and with the new 1.2 soft cap rules don't count so you want them to be the expensive ones (I pray for tanks rather than infantry). In comparison to standard units they have 1 extra attack power and one less defence so they will tend to hurt the AI more but also are more likely to take casualties in return, one reason over-strength on them in the deployment phase will help keep them viable longer.
Experience. To me elite replacement is essential as experience has a bigger effect on combat effectiveness than over-strength in a lot of ways. Some will argue that in GC39/40 you don't need to elite reinforce as you will reach the exp cap anyway, but i'm usually using these scenarios to gain experience on more units than I need so I don't have to add green units to my core in GC42/43. Why is experience so valuable, well the table in this thread is a good place to look.
viewtopic.php?f=125&t=42325&hilit=unit+experience+table
For each 100 exp (1 star) a unit gets the listed bonus, better attack and defence power and critically higher initiative, for each 1 point of initiative higher than the opposing unit 20% of the unit you attacks strength cant shoot back!!! So say as green units they have the same initiative, a 2 star unit against the green unit now has 1 higher initiative so rather than 10 v 10 dice rolls it will be 10 v 8 in the experienced units favour, that's actually slightly better than the 12 v 10 you would get with a 2 over-strength unit and even better if its infantry v infantry your 2 star unit has 2 higher soft attack, 2 higher Ground defence and 1 higher close defence than the 2 over-strength one (the difference between FM and General difficulty of player exp 50% vs 100% looking more logical now?). I would say studying the combat mechanics threads are well worth it, a good place to start being.
http://www.matrixgames.com/forums/tm.asp?m=2994803
Ok what's next, Terrain. Infantry in the clear Blah, Tanks in Trees double Blah!!!. Where you place your units for any particular combat will dramatically affect their ability to hold and the casualties they will experience. A poor infantry standing in the open getting attacked by most tanks is going to be in serious trouble, but put them in the trees (any close terrain hex) and the tank will think twice about even attacking. Even between types of close terrain some are better because of the initiative cap effects, hills are probably the best close terrain choice of all. where there is a choice consider where each unit type in your defence will stand, it may be worth retreating a hex or two when faced by a serious counter attack to make killing it off easier, and then continue your advance later. Think about the order units should attack in, which direction the attacked unit may be forced to retreat (onto which type of terrain) and when to throw in air or artillery attacks. Better players are always looking at 3 things, how to make an AI unit fight on unfavourable terrain, how to set up a chance to force a surrender for the lovely prestige bonus and should you attack, even if you cause free casualties, if it causes the unit to retreat and leaves it where none of your units are restricting its resupply/reinforce opportunities (remember an entrenched unit wont retreat).
As a final point artillery cover. An artillery unit adjacent to any other unit provides suppression fire in support of that unit if its attacked, as many times in a turn as it has ammo, the suppressed str of the attacker doesn't get to fight so its big smiles all around. Though later in the game the benefits of artillery become less, artillery suppression is you big friend early on in limiting casualties you take, ofc it needs to be in deployed mode rather than transport mode to have any effect at all.
Sorry if I've covered stuff you already knew, but you not focussing on getting good exp levels on units where possible by suggested a broader overview of things to consider might help.
Have fun
Bonesoul