The Imperium has a much better selection of company commanders than the Orks, and does not need to worry about "nationality" as much as the Orks do (the main exception being the Space Marines).
Generally, the Imperial player is better off standing back and letting the Orks come to him. As the Imperials, you should ruthlessly bombard the Orks with artillery and long-ranged weapons before they close the distance, where their superior close combat skills will overwhelm you. Likewise, it's almost impossible for the Orks to win a shooting-match against you, so try to force them to do just that whenever you can.
Still, you will need something to protect your long-range units and fight the Orks up-close. That's where your Super-Heavy tanks excel, but they'll need the support of your other vehicles or infantry. Units such Thunderhawks or Warhound Titans can be used for lightning counter-attacks against an unsuspecting Ork opponent.
Infantry tactics[]
Imperial infantry is generally inferior to the Orks, the two exceptions being Imperial Guard Heavies and - to a lesser extent - Space Marines. Their slow speed means they should be used to hold ground, or be mounted in APCs or Thunderhawks.
Space Marines are your only good attack infantry. They are accurate, have a morale bonus, and have decent CA. Still, they're no match for Nobz.
Heavies are very useful due to their extended range. The good thing about this unit is that it has the advantages of infantry (can enter forests and buildings etc.) and yet is powerful enough to take all enemy vehicles except heavy tanks.
The Tallarn Captain also deserves a mention here. Basically this platoon is one guy squad with pistols, but which also helps reduce the suppression of nearby units and four Heavy squads.
Rough Riders have a decent CA, but are very vulnerable and need special unit slots. They are also slower than the Ork bikes. They're really only good for defending your artillery - don't expect them to take the fight to the Orks.
The other units aren't nearly as good - Tacticals and Planet Guards are weaker versions of Space Marines, but only slightly cheaper. Assault guardsmen are simply not strong enough to take on Orks in CA. The Commissar and other Captains are only good for raising morale - they just aren't a match for Ork infantry.
Vehicle tactics[]
As a general rule, Imperial vehicles are slower and more expensive than those of Orks, but have more firepower and armour. The Imperium has a wide selection of artillery and tanks, but few light vehicles.
Your vehicles can be broadly divided into the following categories:
1. Artillery - as in the real world, these are the greatest killers on the battlefield. They are usually slow, lightly armoured and very vulnerable if the enemy gets close to them. On the other hand, they have long range, are deadly against the right targets, and are often surprisingly cheap. Remember artillery can fire only once per turn, and cannot move more than 1 square before firing (this also means suppression will effectively prevent them from firing).
Examples: Basilisk, Bombard, Manticore, Whirlwind, Thudd Gun. The Deathstrike Missile is similar, but cannot fire without a line-of-sight to the target.
2. Battle Tanks - these are heavily armoured, have average speed and out-gun most Ork vehicles. Unfortunately, they are also very expensive, and will quickly get overwhelmed in Close Assault. They are best used to engage Ork tanks and light vehicles In terms of raw firepower and staying power, Super-Heavies are usually a better investment. But battle tanks are much more mobile.
Examples: Leman Russ, Demolisher, Predator, Land Raider (also an APC), Vindicator
3. APCs - The main problem with these vehicles is that they have light armour, which makes any troops inside them very vulnerable. Still, the Orks have little in the way of artillery, so the Imperium can actually make better use of their transports than they can. I'd recommend using only Chimeras - the Land Raider is just too expensive for what it does, while the Rhino is practically unarmed and thus cannot help support the troops it disembarks.
Examples: Chimera, Rhino, Land Raider (though it usually gets used as a Battle Tank)
The Hydra and Hellhound don't really fit into any of the above categories. The former is only used to defend against aircraft, while the Hellhound's weak weapon and armour make it rather useless.
Super-heavy vehicle tactics[]
Super-heavies are slow but have extremely high firepower. They also have strong armour, but are vulnerable to a few special weapons, such as Lifta-Droppas, Pulsa Rokkits and Fighta-Bommerz. They'll also have a hard time against any Gargant (other than a Stomper). They are much better than their Ork equivalents. Because of their high cost, low speed and large size, super-heavies should be positioned very carefully, or they may end up spending half the game moving into position!
Generally, it is a good idea to have your super-heavies work in pairs, or to protect them with cheaper units, so that they don't get outflanked.
Compared to the Orks, you are spoiled for choice in this category. Still, I'd argue one vehicle is much better than the others: the Stormhammer. This beast packs more punch than a squadron of Leman Russ tanks and yet costs the same. It is also extremely lethal close up with its array of bolters and high CA.
The Baneblade is a stripped-down version of the Storm Hammer: less guns, but cheaper. You'll probably want to buy at least one in the campagin since Storm Hammers aren't available immediately.
The Shadowsword simply doesn't have the same volume of firepower as the other superheavies, and is actually rather vulnerable up close. While not a totally bad unit, I'd not shell out so many points for what's essentially three Lascannons, one of which has a longer range than normal.
The Leviathan looks impressive on paper, but really isn't. If you use it as a transporter you're wasting its firepower - and it's no faster than the infantry it carries; similarly, if it uses the Doomsday cannon, it can't move that turn. Its Lascannons and Bolters all fire as a single weapon, which doesn't seem to be nearly as powerful as it should. The Leviathan is expensive, and it tries to do a lot of things and isn't particularly good at any of them - meaning whatever you do, you're wasting points. The only bright side is that it has respectable armour even on its sides and rear, and 4 void shields. Still, a single Pulsa Rokkit or Lifta Droppa can one-shot-kill you.
Flier tactics[]
Again you have more choice than the Orks. The Marauder is effectively identical to the Fighta-Bommer. Your other two vehicles are very different, because they do not fly off the battlefield after every attack.
The Marauder is best used to destroy Ork Pulsa Rokkits before they fire, and then against the other dangerous vehicles like Kannon Speedstas, Lifta-Droppas and Nobz Warbikes. Stay clear of Flakwagons - leave destroying them to your artillery. You can even attack Gargants in from behind if you're feeling daring - though be careful of Orks hiding behind buildings and hills!
Land Speeders are very fragile, but potentially very powerful if used correctly. Hide them until needed - patience is the key. Remember they have a high CA score!
The Thunderhawk is potentially very powerful and versatile. It's the only flying troop transporter in the game, making it good for objective-grabbing. It can move and fire it's battlecannon/rocket combo in the same turn, and it doesn't even need a line of sight. However, it is also very vulnerable, particularly to Fighta-Bommerz.
Titan tactics[]
The Imperium generally gets better Titans, too. Or rather, their Titans are better against Ork Gargants than vice-versa. While they have less shields than their Orkish equivalents, titans can self-repair their shields (this is done automatically each turn and is somewhat random).
All Titans are vulnerable to Pulsa Rokkits, Kannon Speedstas and, if attacked from the flak or rear, Fighta-Bommerz. Also remember that even the Warlord can be overwhelmed if multiple units attack it in the same turn.
The Reaver and Warlord titans have a very wide variety of weapons but are usually best suited to anti-tank or anti-gargant duties.
The Warhound is particularly interesting since it's very fast and one of the few Imperial units that can reliably take to the offensive. It's also cheaper, but not nearly as powerful as the other two titans.