This is the base class that all my entities are based on:

 

public abstract class EntityCustom extends EntityCreature {
    public EntityCustom(World world) {
        super(world);

        this.setHealth(20);

        // This method makes the mob not despawn
        this.func_110163_bv();

        this.tasks.addTask(0, new EntityAISwimming(this));
        this.tasks.addTask(1, new EntityAIWander(this, 1.0D));
        this.tasks.addTask(2, new EntityAILookIdle(this));
    }
}

 

Even if I set the wander speed to 4.0, all mobs move at the speed of a person sneaking while blocking with a sword.

You need to override applyEntityAttributes(). In that method, add this.getEntityAttribute(SharedMonsterAttributes.movementSpeed).setBaseValue(some speed);

Great.