Offensive combat tactics
Whenever the game lets you, try to outflank the enemy. Keep a force just out of range of enemy guns in the main (expected) route of advance and send the bulk of your force around one or more sides. The non-flanking units either join in after the enemy positions have been softened up or act as protection against counter-attack.
By flanking, you look for side/rear shots on enemy tanks, and allow your infantry to fire down the trench on enemy infantry.
On the defense, AT guns are absolutely deadly and full frontal assaults on them and entrenched infantry should be avoided whenever you can. (The only exception is when you have no other route of advance - in which case you should use the Red Army tactic of mass tank & infantry rush right amidst the AT guns and finish them off at point-blank range. Melee style!).
If you have access to artillery or air support, then your priority targets are, in this order:
- Artillery / AT Guns
- Massed infantry & dug in defenses like bunkers
The exceptions are if there's a particularly hard position to crack. Wiping out the defenders along the main route of advance with an accurate artillery strike can often allow your forces to charge "straight up the gut" towards the objective.
Overwatch is a tactic where you leap-frog your units (mainly tanks) in an advance. Basically, one unit pauses while the next one advances a short distance and vice versa. This allows the stopped unit to fire on any counter striking force threatening the moving unit - which in WWII, cannot fire back accurately.
Defensive combat tactics
Arguably the harder side to fight (as you are often outnumbered). You need to defend the most obvious approaches to your position as well as their flanks. Dig in your infantry in available trenches or structures and place AT behind them. The AT takes out approaching armor and the infantry are for close-in fighting. If you can, position the AT so that you either get overlapping fields of fire and/or side and rear shots on enemy armor.
You are usually defending a strongpoint like a hill top or a chateau. So if you have armor, place them near the centre. They should act as a fire brigade and rush to repel any breaches. If you have lots of armor, consider placing a tank platoon off to one flank (and put on the Flight of the Valkyries over their loud speakers) to charge into the flank of an exposed attacking force just as they begin to get bogged down by your main defenders. Time this right and you'll have a TSN Turning point as the enemy breaks and runs home to mama.
Artillery (on map and off map) are your best friends on defense. Off map arty is expensive but are worth every resource point if called in correctly. Save your barrages for when it looks like there is a clumped-together force about to breach your lines. As such, you should try to funnel the enemy into killzones and bog them down long enough for the arty to land and obiliterate them. On-map arty will fire on their own but you can also target their fire. Some pieces like the Sherman Calliope fire a barrage and then take ages to re-charge, so use them wisely and keep them out of direct confrontations with enemy tanks and AT.
Game specific strategies
Unlike the real thing, you have three valuable panic buttons: pause, save and (re)load. Use them often.
In the game, General Patton is on your butt about getting the jump on and attacking the enemy and he wants it done yesterday. But even the best generals and colonels look over battlefield intel and study their maps before committing their forces. You should do the same. Because there's no fog of war in Order of War, you should look at every red dot on the map and plan your moves to outflank, assault or bypass them. Also, just because some of those red dots are currently out of bounds, does not mean they can't come to their comrades' rescue. Be aware and leave some units close to home.
Know yourself and your enemy: use the Range function to see how far the enemy can shoot vs your own units' range. Then move your units to minimize damage while your units can hit back with much greater impact.