The Mongols are a strong early game civilization due to their hunting bonus, and their team bonus makes Dark Age scouting far more effective for everyone on their team.
Their Cavalry Archers have a faster attack speed, making them excel at raiding enemy towns or picking off enemy units from a distance. The Mongols have access to all archer upgrades and technologies apart from Ring Archer Armor, giving their ranged units an advantage over many other civilizations. Their light cavalry have extra hitpoints and line of sight, making them very effective as scouts and raiders early in the game, and compensating somewhat for their lack of Plate Barding Armor later. Their unique unit, the Mangudai, is a cavalry archer with a bonus against siege weapons. Their speed and fast fire rate make them very versatile compared to other unique units. Mangudai are difficult to hit due to their speed, so can quickly eliminate dangerous siege weapons that can pose a threat to buildings or fragile units. They have access to all siege weapons except for the Bombard Cannon, giving them a strong offensive edge. Their unique technology improves the speed of their siege weapons greatly, allowing them to participate in raids effectively. A Battering Ram filled with infantry will be able to move at the same speed as cavalry, allowing them to demolish buildings and flee before the opponent can muster a counter-attack. They also have access to all cavalry units and technologies except for the Paladin.
One of the main weakness of the Mongols is their mediocre defense. They don't have much defensive abilities to hold off an attack since they cannot upgrade their towers beyond the Guard Tower upgrade and cannot build Bombard Towers to take control of captured territory effectively. Thus, Mongol players must constantly attack the enemy to make sure they are unable to build up a strong enough force to attack. If forced on the defense Mangudai are an effective way of destroying enemy siege weapons, allowing time to hide behind a wall and build up a counter-attack. Also the Mongols have no gunpowder units except cannon galleons. Their lack of Ring Archer Armor and Plate Barding Armor causes their Hussars and Mangudai to be more vulnerable than they might otherwise be; this combined with their lack of Paladins means that their late game heavy cavalry is very much below par. Despite having access to all the infantry upgrades at the blacksmith, the Mongols have no Halberdiers, which deprives them of a useful late game counter to cavalry and means their infantry isn't as strong as it could be.