Orianna is very reliant on her ball, pick champions with high mobility and/or sustain. When playing against Orianna, take consideration of these points.
Always stay away from the ball, if you run into the ball she'll cast her spells on it. Try to dodge it too. (start with boots)
If she planted the ball near you, try to have minions between you and the ball, it reduces the damage per target hit.
Orianna's spell damage is not super high early game because of that she will try to harrass you despite her mana cost on her q being lowered a month ago or so. She will run out of mana quickly.
Orianna is very squishy, try to harrass her back, after she missed a q. you can bully her around for a few sec.
As i've mentioned before, Orianna can't instantly kill you, she counts on harrassing you to 50% health before actully attemping to attack(thats early and middle game) so if you are willing to have a clash with her, make it fast.
Orianna has such short cooldowns with the right items, not to mention that she counts on the combo of her skills all together so any silence or stun in the middle of her combo will ruin it.
Beware of her passive, it gets underestimated a lot but when she gets a few autoattacks on you, it hurts..
There are several ways to play Teemo (I've seen pure AP, AP/AS, AD carry, support, etc.), although the different styles often have several points in common.
Things you want to do regardless of build
- Prioritize targets - Teemo's Blinding Shot (Q) is a ridiculously strong crowd control effect, but only when used on the proper champions. Blind has little to no effect if you target AP carries or tanks, but it can completely shut down AD champions (Jax, Fiora, and most AD carries)
- Keep shrooms up - Teemo's shrooms are amazing, regardless of build. Not only do they provide vision and serve as an early-warning system, they also have a great CC slowing effect. I've seen several support Teemos help their team to disengage by placing shrooms as they retreat.
AP Teemo in particular should drop shrooms as often as possible outside of combat, they have great scaling with AP and more vision never hurts. However, the small cast range on shrooms means that shrooming during teamfights will generally be a defensive maneuver. Be sure to drop one or two under your AD carry if you suspect that you will be initiated on.
The blind is one thing that I cannot stress enough. I have seen countless Teemos blind the enemy AP carry in an effort to score a kill while the enemy Jax or Fiora rips holes through the team. Do not waste your blind.
You won't be using your shrooms all too often during teamfights unless they engage on you. However, if you notice an enemy standing open in one spot (generally the AD carry), feel free to drop a shroom if you think you can do without too much risk. AP Teemo's damage during fights will come mostly from sustained damage on his Toxic Shot and burst from his Blinding Shot.
Best Answer
Orianna is a control mage, which broadly means her primary focus in a teamfight is to stay at around mid-range and utilize her spells to deter enemies from forcing an engage and apply crowd-control spells to help her team secure kills.
For Orianna specifically, though, her primary form of control is a combination of her Q -> W, and her Q -> R. Her Q -> W is a simple combo that does a small amount of chip damage early, but can scale up significantly as the game progresses, often times dealing ~50% of an enemy carry's health in damage. When an opportunity to apply this poke damage presents itself, you should jump at the opportunity. If the enemy charges forward in an attempt to deal some damage back to you (otherwise known as "trading") you should hold the Alt key and press E to withdraw the ball back to yourself to apply a shield. You can also use your E on allies who are getting engaged upon to mitigate the damage they take.
Your most explosive ability is your R. In a somewhat large area around your ball, you pick up and throw all enemy champions, majorly disrupting their positioning in a teamfight and dealing a large amount of damage. This spell wins games. If you see an opportunity to use your Q -> R (or use your E on an ally that's surrounded and press R, or use your E on an ally that's about to dive into multiple enemies and press R), you should absolutely do so. However, it's important to note that you shouldn't hold onto your ultimate for too long. Some players have a hard time balancing knowing when to hold their ultimate and when to use it. It all depends upon the fight, and oftentimes using it on a single enemy carry alone can win you a teamfight. In other words, don't greed for a high-target ultimate when a one-target ultimate on a high-value target is available.
In summary, Orianna should be played as a mid-range support and control mage at the teamfight phase. As a squishier mage, you should be monitoring the enemy divers and assassins and ensuring that you're safe from their engage tools (jumps, dashes, ultimates) and applying your poke damage where it's safe for you to do so. Shield your allies from chip and engage damage, and make sure you can get off a high-value ultimate cast, ideally when following up on a tankier ally's engagement, but mostly when an opportunity presents itself.