Elephants and chariots were used for war before Dimas and Gestas died on a cross. Well, long before they were born. If you use them wisely, they'll give you decisive victories, like to Hannibal. If you use them badly, you'll have expensive loses, like Antiochus III.
As they are very expensive units, they have to be used wisely and they have to be protected from units that counter them, i.e., they have to be protected from enemy missiles and spears.
Finally, both chariots and elephants must always be moving.
Elephants are beautiful and clever animals, but they can be horrific on the battlefield. They are useful to finish off all kinds of infantry (be careful with spears, be extremely careful with pikes and keep them away from enemy arrows).
How to use elephants
I'd say that the main difference between a game and a real battle is that orders are instantaneous and unequivocal (I'd say, because, luckily, I've never been in one). This gives a lot of maneuverability in the game and allows the use of more subtle tactics. In the diagrams below you can see one of the best uses (if not the best) you can give to elephants.
In this battle, we have invested on elephants and our left flank more resources, so probably our core is weaker, thus it is very important to play aggresively on the left flank so that the elephants have enough space to maneuver before our infantry is lost. It's important that our right flank units can hold their ground, so a combination of cavalry and spearmen would be the best.
I'm aware that all this text about the composition of the army to take the most of elephants should go on the strategies section, but I didn't feel as I should divide such an intimately relationed content.
Chariot units are specially useful against light units. This is due to the fact that they do damage when they go through the units, but they got stuck in heavy ones as in a swamp. For this reason, the best use you can give them is to walk them through the enemy's less armoured units, and if those units are expensive, better.
So it's very important which army you are facing: chariots do more damage when they go through the lines of the brave (but weakly armoured) lusitani than when they got stuck on a roman legionnaires unit (against Rome I'd pick elephants). Combine this tips with the cavalry ones and there will be no men with harmless ankles.