I've had an easy time finding some good basic techniques of Halberd vs Halberd, but I'm having trouble getting a good idea of how a Halberd fighter would fight against someone with a sword, or axe, or sword and shield. Google doesn't show much, except for 2 videos that have someone with a halberd that's more akin to an oversized axe.

Similarly for pollaxe and partisan, most of what you see will be for like-against-like.

Against the short weapons, you have reach. Move to the distance where you can hit them with a stepping-forward thrust. Your opponent won't stay there. If they do, step in and poke them. Feint a rapid close and thrust. They might move back and stop. When they're recovering from that, close and thrust. They might try to block and close, or sidestep and close. You're ready for this, so you loop your point in and thrust. That's all useful basic strategy for long thrusting weapon against short. Works for spear, partisan and two-handed sword. Why wouldn't it work for halberd too?

Try to engage, trap, or immobilise their weapon with the head of yours. Spikes, flanges, hooks etc are there for a reason. This is the way to close with an opponent who has a longer thrusting weapon. Can be useful against short weapons too, especially single-handed short weapons.

Against sword and shield, don't have your weapon pinned for pushed aside by their shield. Be careful! If they rush you, thrust for their face - up goes their shield, and then they can't see very well anymore. Go for the foot, either to thrust/trip, or cut from the side. Hook their shield down and towards you with your blade or back spike, followed by a thrust to the face if they cooperate by pulling their shield back to resist.

If they close, throw them, or grapple standing. You can try to keep the halberd in one hand, or just drop it. Just keep it in both hands if you can throw them without letting go with either hand. Are you wearing armour? Are they wearing armour?

None of the above is specific techniques - the specific techniques will be the specific techniques that are taught in the context of halberd vs halberd. The key difference will be the difference in range. Unless your opponent leaves you safe by just trying to stay out of reach, you will have a very nice window of opportunity to hit them as they try to close rapidly. It might be a very brief window of opportunity. Use it well.

A battlefield would be a different story, fighting with halberdiers to your left and right as well. Opponent tries to close, three of you can try to stop him. One puts a point in the way, that stops him. If the point is merely in the way, instead of in the opponent, number 2 immobilises the weapon (or arm), and number 3 hits them.

In addition Timo Nieminen's comments which deftly cover pretty much everything I could say from my own experience, I recommend the book Polearms of Paulus Hector Mair, there's a large chunk specifically on halberd use and segment on mismatched weapons such as halberd against spear or rapier that could prove useful.

http://www.myArmoury.com/books/item.1581606443.html