"God is for the big battalions"
-- Voltaire
Wars ain't fair nor pretty, so stack the deck in your favour:
3-1 advantage is not "an overwhelming force". An overwhelming force is 10-1 with you having mech infs and the other civ having spearmen. If "overwhelming" is not possible then go for the adequate 5-1...
When you go to war you go to war. Politicians not totally committed to the war effort have brought ruin more than enough times in the real world, you know

. Thus all of your cities should produce units/improvements that are directly useful in the war. And they should continue doing so right until the opponent is utterly crushed.
Exchanging your numbers against the opponen't quality is ok if your production is up to it. If you can crank up your production to 12 units / turn while your opponent does 4 units / turn then you can keep on exchanging 2 to 1 and win. The number below the final tally line is what counts. War Heroes beat the Industrial Generals only in the novels.
If it is bad to the enemy it is good to you. Pillaging his road network will hinder his troop movements, disrupt trade, and if thought out carefully cut him off from his strategic resources. Besieging a city will dislocate the workers from the tiles causing production loss and starvation. Blockading the capital (if it has a harbor) and pillaging the surrounding roads will disrupt his trade network entirely.
Also, when you commit to a single attack or battle it is for a purpose that will gain you something. Losing units in a battle that only costs some hit points to the enemy is pointless if he can heal his damage in a single turn. This is called concentration of force and it is why you will attack a fortified position with at least a 4-1 advantage. If the enemy is left weaker and you made stronger because of your attack you scored a victory. Otherwise you are the loser. And this is completely regardless whose units were left standing on the battlefield.
The converse is also true: if the enemy keeps banging his head against your strong points losing units without gaining anything it's a victory for you. Terrain and fortifications combined with good defenders can give lots of headaches to the opposite generals. As a specific case: settlers ought to be a part of your army. A city can also be thought of as a military base. With barracks it heals your units and after you have rushbuilt the airport you can bring in troops with ease. If you don't need the city after the war then just abandon it.
Doctrine of advantage: grab it wherever you get it. Attack where the enemy is weak. If the war is fought on one front and your opponent is concentrating his forces there then a special force landing behind his lines can do wonders or at least pillage and rape his countryside. With luck it can also force the enemy to split his forces to deal with the secondary attack making him weaker in the main front. Which allows you to strike there. Or if he does not comply, then no sweat, because then the diversification attack is the main attack and continues its pillaging and torching.
This is also why I think having a good navy is essential, although some have doubts about its usefulness. Controlling the seas allows me to strike at will where I want while at the same time I can keep *my* backside covered against *his* sneak attacks.