As I mentioned in the comments, you're looking at the wrong aspect of armor. You shouldn't be looking at the percentage it reduces, but rather the amount of damage it actually prevents as a measure of how much longer that armor lets your survive.
Let's consider an example for a champion with 0 armor. Say he has 1000 health, just 'cause that's a nice round number. Now our champion gets caught in Garen's judgement, and starts taking 100 physical damage each second (at one hit per second). Clearly, our protagonist can take ten hits before dying.
But now, imagine our champion has the 50 armor you mention, meaning the incoming physical damage is reduced. Now (still with 1000 health) it takes 15 seconds for that bastard Garen to claim our champion's life. 50 armor extended our life by 5 seconds. (100 * (2/3) = 66.6 DPS; 1000 / 66.66... = 15 hits)
So our champion respawns, wises up, and buys 50 more armor. Now with 100 armor, we're sitting at a flat 50% damage reduction. Again we run into Garen, who's still dealing 100 base damage per second. It now takes him twice as long to kill us -- 20 seconds. Once again the armor has extended our life, again by 5 seconds. (100 * .5 = 50 DPS; 1000 / 50 = 20 hits)
Back in base, we buy another 50 armor. We're now at 150 armor, and 60% damage reduction. Enter Garen -- spinspinspinspinspinspin and it takes 25 seconds before our champion dies. Again, adding 50 armor extended our life by 5 seconds. (100 * .4 = 40 DPS; 1000 / 40 = 25 hits)
So even while the amount of damage reduced per point of armor diminishes (as you observed), the amount of time armor extends your life (or effective health) remains distinctly linear.
Okay, from my experiments, it goes:
Armor/MR reductions <--> Percentage Reductions
(They stack multiplicatively, so order is irrelevant)
Flat Reductions
This makes sense, since if flat reduction was the first thing applied, after armor, it may have failed to provide a benefit at all (since, for instance, the difference between 50 * 27% and 48 * 27% is minute at best. 50 and 27% being the base attack damage of Ezreal and the armor of Amumu, my two test characters.)
Shields act as health, and damage done to shields is likewise reduced by armor / magic resist. (Meaning shields on tanks can generally absorb more punishment than shields on squishies)
Best Answer
The most important part about playing squishy champions in lategame is positioning. You're not the super beefy frontline that just chases everyone down. Especially on champions like Orianna and Xerath where you have absolutely no escape spells. In (lategame) teamfights you should almost always use your flash defensively and/or to reposition yourself.
If you're playing these "classic mages" your main tasks are: crowd control, poking, waveclearing and killing the other squishies.
Crowd Control
You basically should use your Crowd Control Abilities to simply lock down everyone who is a threat. You can use it to peel for your other Squishies in the team, but also to secure a potential kill on a target that's out of position. If you're playing champions with AOE CC (like Orianna) you should also try to use your CC spells to melt down the entire enemy team at once. Usually in combo teams this allows for easy kills on high priority targets while after that your ADCs can kill the tanks.
Poking
A lot of classic mages can also poke really well. If you play one of those (like Xerath) you should simply spam your spells to bring the enemy team low before the actual teamfight begins. Here it's not as important as in teamfights to focus a high-priority target but it's still recommended. Also if you're fighting for jungle objectives like Baron or Dragon, you can completely change the outcome of the fight before it even begins simply by poking all the time.
Waveclearing
Usually Mages have really good waveclear and a lot of people forget how important this is. Obviously it's really useful for pushing but it's even more useful for defending turrets. If the enemy team has no minions an engage on you will be a lot harder since they cannot position that easy without taking a lot of damage from turrets (yes even lategame tanks take damage from turrets).
Killing Squishies
Of course this is basically your main job in a teamfight. This is essentially a combination of all of the above. Usually you don't even have the target directly but you can also force them out of a fight. To kill one of their squishies you'll usually have to find them out of position which isn't always that easy. If you can't do it (maybe because the enemy ADC positions himself very well) you can switch over to the next highest priority target that's in range or just bring some AOE damage/utility.
A last word: Most mages aren't that strong in lategame. They are mainly built around Mid-Game teamfights.