If you rent elephants they are most effective if you turn off their normal skirmish mode and charge. They will squash the enemy as they do when they run amok.
When the Timurids attack your cities/castles put some archers to shoot fire arrows at them and when the elephants who always seem to walk up to the gate and sit there doing not much of anything run amok they may do tremendous damage to the AI's infantry and even the Horse archers running around in circles. It is quite amusing, if you are not a Timurid. If you rent elephants be sure to stay away from flaming bolts from ballista. I lost both units of elephants to them before the battle even really got started (probably a very rare happening but they are not as invincible as they seem). If you pin the elephants with any kind of unit and get them stopped and then you get an effective charge into the rear of the elephants with Hospitalers or such you can kill some or even all or get them to run amok, but it will take several charges unless they are already weakened. (It is really hard to catch them with pikes and when you do it won't do any good unless you have removed the pikes secondary weapon or are playing a mod which has done this.)