IMO, depending on the animal, it could be faster than some vehicles. Remember, we're talking magic here. You'd probably catch up with the slower ones, but those badass body fueled bikes should prove a problem.

A mecha wolf would be more of a futuristic ride. A bit way too technologic advanced for the setting.

My sugestion would be an annimal in full armor that is decently fast but also can jump. You lose speed, but gain not only combat effectiveness, but also versatility. My sugestion? A full plated giant quaggoth. 
[hider=This fucker]
[img]http://dungeonsmaster.com/wp-content/uploads/2015/09/quaggoth-01.jpg[/img]
[url]http://forgottenrealms.wikia.com/wiki/Quaggoth[/url]
[/hider]

Usually they stand 7 feet tall, but to carry an orc you would need more, much more. Make something up to have him being a dumb giant and you're good.

On the top of my head I'd go with:
- Your family/tribe breeds them with various species for various purposes. Your's happens to be a mix with a giant, used for mounts. This would also explain how your family/tribe is trying to adapt to the new thingies called vehicles while staying as close as possible to the Orc's principles.

- You stole it from a crazy Drow who was experimenting with it. The Quaggoth is frenzied, but recgonizes you as it's savior, so it allows you to mount it. Nice little relationship as in Dragon Age origins with the Dog.

- It was born this way and as such, expelled from it's tribe. When you found it a connection was immediatly forged, as you are also an outcast from your own tribe.