Your best strategy is raiding, but when you must face them on the field (and you will, of course, it's unavoidable), you must be aware of two things: Southron Lancers are death incarnate and Muhad Tribesmen are close behind. If you try to fight Harad without Gondor Spearmen, you will suffer - the Lancers will just ride you down.
If you are able to charge Southron Lancers with Gondor Militia Cavalry,
without the Lancers charging you, you will win in the ensuing melee. If they charge you, you will either lose, or win with such devastating losses you might as well have lost. A General's Bodyguard can inflict massive casualties against Lancers, but not enough to win the subsequent fight if they can't run away. Imrahil's Bodyguard, on the other hand, will flatten a unit of Southron Lancers like a pancake. Use appropriately.
It's usually not safe to use cavalry against the Muhad Tribesmen until late in the battle, due to the presence of Southron Lancers or Serpent Guards. Archers are your only real option.
So how to deploy? Well, for fighting Harad, if I don't have archers with stakes (Ithilien Rangers, in FRoGS I use Dol Amroth archers, MOS probably has options, too) I use a
Byzantine deployment. A thin line of Gondor Spearmen in the center,
immediately behind which are swordsmen (militia or, better, Pelargir Marines - the Gondor Infantry should be fighting Mordor) and behind them, as many archers of the best type I can find and afford - a
minimum of four units. Cavalry on the wings - at least two units per wing, three is better, militia is fine - screened by more Gondor Spearmen. If you have stakes, you can dispense with the central spearmen, and deploy your archers just before your swordsmen.
As annoying as Harad's archers and Muhad Tribesmen are, your first priority
must be to destroy their cavalry. Only when they are gone, focus on the enemy archers/Muhad Tribesmen.
Do not engage infantry with your Spearmen, they are only there to fight cavalry. If infantry is moving against your center, counter-charge with your swordsmen. The enemy can't deliver a charge through their own men, so you're safe. If infantry is moving against the spearmen screening your cavalry, engage them, but only while you run a unit of cavalry out to flank charge them... break them before they inflict many casualties and then withdraw the cavalry back behind your spears if the enemy still has Lancers in service.
Once your archers have reduced the enemy cavalry down to half strength or so, it's time to move your cavalry out and finish them off. Focus your archers on unengaged enemy cavalry or on enemy archers/Muhad's.
The presence of Mumakil obviously change things. Focus your archers on them with fire arrows and move your Marines to kill them ASAP, then try to return to formation if you can.
You will take losses against Harad, sometimes heavy ones, but you shouldn't ever lose more than you can afford to replace quickly, since you should probably be relying mostly on Militia Cavalry and Infantry for the majority of combat.