A little problem with war machinery like ballestae and catapults is that they weren't very easy to aim. The only way to hit the spot you wanted with a catapult was to shoot repeatedly until you hit the mark. Also, you would usually be aiming at a big, tall wall rather than at a comparatively small fell beast. Ballistae I'm not sure but I would guess they were not aimed at all (besides towards the marching lines of the enemy) after all, with one ballista shoot you can probably take down a bunch of people at once. Even if ballistae were "aimable" it would not be an easy process as the fell beasts would be moving around. Archers would be the best choice yet it is said they stayed out bow range.
Biological warfare is a tricky subject, as orcs and humans probably have VERY different immune sistems and I don't know who (outside of Mordor) knew enough about orcs to know what would make them sick. Furthermore, it is possible that whatever makes an orc sick would outright kill a human. And then, how do you deliver your pathogen? say, rotten food... will you invite them for dinner?
Poisoning a river could be, but you would need an awful lot of poison, assuming it works on orcs...
My solution? take the bus into Mordor, get off at Mt. Doom station and destroy one or two "The Ring"'s
Oh, that's not how it happens?
then I would guess just try to hold them back with fire and Gandalf, and pray for the best... after all, it is likely that they do not have many fell beasts so even if you loose a few soldiers for each of those you kill, it might just be worth it.