Since you don't stand a chance at the beginning, pull your peons over to the southeastern base where grom is. Get your economy up and running there because the elves will destroy the other bases across the river. The Elves are going to attack this base when they're done with the others so you should make a decent defensive force. Fortunately there are plenty of burrows to supplement this and if you get extra peons on the gold mine quickly you will have enough resources.

Notice that you have the 15,000 wood when you begin. So you don't even need to have peons doing that, really. Build grunts at the barracks and witch doctors at the spirit lodge. Send one group to the north and keep one where the peons crossed the river. These locations are where the elves are going to begin their attack. This is not too hard as there are plenty of defensive structures around you base. When you're done you can begin to prepare a counter attack.

Before too long you get the above-mentioned quest. Before you go venturing off though, don't forget that you have a base to defend. Keep a nice balance of air and land defense there as you never know when the Elves will attack. When you're ready take your attack force and at least one catapault and head to the north of your base. There are some dire wolves (drop nothing) in your way but they shouldn't be too difficult. Use the catapault to destroy the growth of trees blocking your path to get to the furbolgs. They don't drop anything, but you do get access to the merchant there. I recommend buying a scroll of protection or two if you have room. With better defense and a healing ward your grunts can really take some damage.

Head a little more north and you'll encounter some more furbolgs. They drop an anti-magic potion and a claws of attack +9. You may want to use a scroll of protection before you start the fight though. You can always go back to the merchant and buy another. Now follow the path around to the west and you'll encounter a group of Satyrs. They're not as powerful as the furbolgs, I felt, but they drop a better item: A periaph of health which will increase Grom's hit points by 300 while it's held! It's a very nice item. Wait until the curse wears off (assuming the Satyr cursed you) then head through the waygate. You'll find yourself behind the elven bases. Sneaky, huh?

Ok. Go a little southwest and you'll encounter some more Satyr. They drop a healing potion, blah! But cross the steream and head to the north and you'll encounter a Satyr Pyromancer who drops an orb of fire when killed. That's much better! Now go north under the arch and you'll come to a rather large, but weak group of skeletons. Kill them and head around the corner to the east. You'll pass a fountain of healing (use it if you like) then continue on the path and you'll reach the chaos well. Time for more corruption! Grom drinks from the cursed well and becomes rather powerful. His attacks and all your grunts' attacks will now deal chaos damage. Also you can build the chaos grunts at your barracks.

Return all your forces to your base and prepare to assault the Night Elves. I used grom's wind walk ability to find Cenarius and he was in a grove on the west side of the map surrounded by all the other bases. So yeah you'll have to deal with him after the others as Grom can't be powerful enough to take him out alone. I got Grom killed to discover this.

First concentrate on the base just west of yours, which is the light blue one. With chaos grunts you won't have too much trouble here, really. They do great damage to everything. Take a kodo beast with them as well as Grom. Don't forget that the elves can build flying units so take some witch doctors and headhunters as well. Build just one chaos warlock from your spirit lodge to cast cripple on cenarius when the time comes. Leave this unit at your base. The purpose here is to have it at full mana when you're ready to use it.

Destroy the bases one by one. Go in this order - Light blue, green, teal. When I got to the green base I encountered many chimeras as they have a roost there. I highly recommend you either many anti-air capable units or raiders. I recommend the raiders. When I began my assault everything was going very fine. Unfortunately before I finished a large demon came and ended the mission. I won't spoil the dialog for you though.