The grunt of the Rohan army is the peasant , of which only one should be kept for repairing structures. Rohan's backbone is the rohirrim warriors and archers. Elven warriors are very versatile units for Rohan as well. Ents are very powerful and cost few command points.
Rohan's main advantage is their heroes. They have Aragorn, Legolas, Gimli, Theoden, Eomer, Eowyn, and Merry. All these heroes have unique special abilities and powers. If you have an ent moot, Rohan can produce Treebeard. Treebeard is a sniper--hero, for his most powerful attack is his long rock-throw. His health is highest, at 6000 points. Gimli has 3000+ health and can deal a lot of melee damage. Legolas is a very powerful archer whose hawk strike is extremely useful early on in the game. Theoden, Eowyn, and Eomer, provide leadership to Rohirrim, and Merry is able to sneak up on lairs.
A different tactic on camp maps is to fully upgrade a peasant army, support them with archers and overwhelm your enemy.
Rohan Peasants: Trained at the Farm, and repair buildings
Rohan Archers: Trained at the Archery Range. They can occupy towers and attack the enemy from there.
Rohirrim: Trained at the Stable. These cavalry can use their spears to attack, but mostly just run over their foes.
Rohirrim Archers: Trained at the Stable. Use bows to attack, whether running towards or from their targeys, or just run over their foes.
Elven warrior: These warriors are from Lothlorien, and appeared at Helm's Deep in the Two Towers film.
Ents: The 'catapults' and heavy duty units for Rohan. They throw rocks at enemies, or can melee-attack them. They are very vulnerable to fire arrows.