Actually, the jaguar standard is less dangerous than if the steg had the Banner of Might. If it had that, it could strike back much harder if you charge it. The Jaguar Standard give the Steg a longer charge range, but you can still deal with it. Obviously, the thing you want is to avoid getting charged and dealing with impact hits as well as regular attacks. This is how:
Make him come to you. You have excellent missle troops. Lay down a lot of archery on the steg and kill some crew. You may not kill it all, but it will make him move forward rather than sit back and get shot. Have either chariots or glade riders set up to charge the steg as soon as it comes within range. Due to steg's lack of rank bonus, you should be able to beat it and make it flee. If he doesn't move within range of your chargers, he has to sit back and get shot up. Of course, if he has a skirmish screen of skinks in front of the steg, you may have to shoot it up to panic or remove them to clear a path for your charging chariot/cavalry.
Warhawks with a strong character can also be an option, since you don't have to overcome a rank bonus.
Last, the steg only has a weaponskill of 2. Attack it with anything with a WS of 5 or more, and it will have a hard time hitting you back (that's why I always take the Banner of Might with my steg). A character in a chariot can do a real number on a steg.
As long as you can manage a charge, the Treeman should win the combat... Getting the charge can be done by using a sacraficial character with less then 5 wounds, (no panic tests are caused for the death of a model with less then 5 wounds). A level 1 mage is a good option, as it is almost certain to die.
If the Treeman charges, the Skinks will be effectively taken out of the fight as their Strength of 3 cannot save them. Only when they charge and use their spears for S4 are they able to wound.
What will this do for you? Well the Treeman with WS8 will be needing 3's to hit with his 4 attacks whilst the Steg will be needing 5's to hit with his 5. The respective Strength and Toughness of each creature will see both wounding on a 4 if they hit, but the Treeman has the advantage that he can also get easy wounds on Skinks if he hits one. This can be all important for getting the combat res. The Treeman will save on 5+ whilst the Steg will save on 4+.
Never ever use the Treewhack... why? Because effectively the blow must be against the Howdah, and it is indestructable.
**Remember**
The banner on a Stegadon's Howdah is not a regimental banner and thus they cannot claim +1 Combat Resolution. They may only utilise the magical properties of the banner, in this case the extra d6" move and the 3d6 pursuit.
If he puts a character in the howdah of the Steg, then destroying it just became all that more easier. Why? Because a character in a Steg, whether Champion, Shaman or Hero *must* accept a challenge if issued... (I think this was clarified in White Dwarf # 215). When accepting the challenge he will Dismount from the Steg and fight on the ground. Again clarified in the above WD issue. Simply charge a reasonable character into the Steg, preferably with some nasty weapon such as the Flail of Skulls or something. Issue a challenge, fight the challenge, score big on overkill and then break the Steg and run it down. It only flees 2d6 with the Jaguar Standard as the Gods are upset at it fleeing. If your character is on a flier or steed, your 3d6 should get him...
The superior charge range of your horses is the key here. Even with the Jaguar Standard, you should be able to hit him before he hits you.
Your cav is a bit of a gamble, as the Steggie might mulch a few of them - but hopefully the lance hits will kill a few skinks and maybe wound the steggie once, and if you do it right you might have flank bonus and a standard (War Banner if you can get it is great here, too) to help out. This is one of the few cases I recommend using the shock cav version of the Riders, but be careful about using heroes and generals and such in there since they won't be able to feign flight out of trouble if the Steggie doesn't break!
Shooting is not so great, IMO - it will take a long time to kill all of the skinks - esp. if your opponent has crammed 5 or 6 of them into that howdah! You will have to focus all of your firepower almost exclusively on the Steggie if you want to get rid of it this way.
Oh yeah - there is also the "Wardancer-Treeman trap" tactic. Just put your wardancers (probably a bunch of them in this case - 7 or 8) in front of the Steggie and absorb the charge with shadow's coil (sure you will take a few impact hits, but you won't flee anywhere!). Then, charge in with the treeman, preferably in the flank. The treeman will cause a few wounds, and the Wardancers might too if they hit a bunch of skinks. And your opponent will need 5's to hit you - you should win this combat pretty easily. This "trap" is useful against lots of heavy hitting troops, so even if you don't fight the Steggie with them they are still worth having along!