Mythago's got a great idea with the dam - but let's take that a step further.
Build the dam upriver, if it's possible, of that pesky elven keep. Do this by clear-cutting everything about 100 yards from the riverbank, which is about as far as a bowman can shoot, yours or theirs. It doesn't seem to make a lot of sense, having a lot of orcs besieging the fort, as long as there are enough, to make sure no one's ambling in and out. The orcs might not like all the work details - kick them until they do, and make sure every orcy labor gang, at least 50 workers strong, is guarded, preferably by a squad on a raft, in the river. Now you've got a lot of lumber, to build your dam. Try to work at night, and rely on darkvision, and again do the construction out of range, of the elven fort. A dam about 20ft high is OK, 30ft is better. You'll have some wood left over - use that to make arrows, handles for greataxes, cooking fires, whatever. The cleaner the banks, the better. You might also want to send some left-over logs downstream, every now and then, just to see if they hit and get stuck. If there's a part of the river you're not travelling through, post some logs, vertically, just below the water's surface, and clip the tops off, at an angle. Any elfy boat that hits one will capsize or get a hole in the hull, or at least come to an abrupt stop. Got your dam ready? Good.
Blow the dam. Swim, little elves, swim. Since you don't have dynamite, just yank some timber out of the bottom, done by some ogres with chains, or a big battering ram thingy.
You probably won't wash away the fort, but you'll ruin all the stores inside, along with any planted crops in the vicinity. A tree that's just partway underwater for a couple days will die, probably just as fast as you can burn them out. The banks will have eroded, making the river flow faster, and be all silty and rank. Areas that are too high to flood, you might try tunneling into, killing the trees you uproot, and forcing them to waste time, locating the burrows. Your pointy-eared opponents will have to deal with impassable tracks, massive outbreaks of cholera and/or dysentery, and soggy silk underpants. But really, this is just to buy you more time, so you can go all Mordor on 'em.
Wherever there's a bend in the river, something that's hard to see and navigate around, put up a watchtower. As big a tower as you can raise, with the legs wrapped in cured animal hide so they don't burn, and staffed with all the orcs you can fit. You might want several floors to your tower, for observation, lobbing arrows, storing supplies, whatever. Keep your towers in contact, with horns and signal flags, using as complicated a code as your orcs can dope out. They should check at least once every half-hour, day or night. Remember, you're not in a hurry, and every bit of attrition is on your side.
Now, you're ready for the final phase. It will take months, or maybe years, but you can connect your towers with suspension bridges, or causeways. This way, even if one tower gets taken, you can isolate it, until you're ready to counter-attack, or you can leave it besieged and keep working. You'll have divided the forest into parcels, which you can methodically wipe out, replace them with orc hovels, a pigsty, a forge, and all the comforts of home. Truly ambitious despots might want to build a permanent castle.
Elves in the forest? Not any more. No more forest. No more elves.