At first, what you must to know when you should choose the Aeon Faction, here are some basic things that you must have in mind, they are important to get right, and you could have large problems if you neglect them:
If you lose air your Auroras are incredible vulnerable to T1 bombers - due to their low hp, up to 9 auroras could die from one pass of a bomber! When you dont have energy to make air, (energy is expensive) make sure that you have 1 Mobile AA +1 scout for 5 auroras in your factory qeue.
The main strength of Aeon at the T1 stage is its tanks - the Auroras. It is strongest T1 unit, but only if used correctly. Auroras have 45% more range than other T1 tanks, but are also slowest and have 50% less hp than other T1 tanks. You can benefit from the range advantage only when you have radar (or a scout). When you don't have radar cover - don't attack with Auroras, because then they are as 50% less effective than other T1 units. The best way to use auroras is to not be too aggressive, always keep them at maximum range, and force the enemy force to move towards your tanks, then go back and try to kite, this gives you more time when your Auroras can shoot them and don't receive any damage back.
Also Auroras have more range than the ACU (22vs26) and most T2 tanks (23vs26) - with solid micro (very solid) you can continuously kite the enemy ACU, and he would need do something with other units or die, becasue he alone cant shoot the Auroras.
The basic aeon strategy is go with acu in front as tank role who will receive damage, have Auroras in back to deal damage. Keep a few interceptors overhead to deny enemy bombers, which are highly effective against Auroras, as they can kill many tanks with one pass.
Aeon have cheap and effective ACU upgrades, they have a gun upgrade that is split into 2 upgrades (2xRoF + 35 range) each for 500 mass and 15000e instead of one for 800m and 24000e. When you decide for make gun upgrade, first be sure that you already have energy storage (its costs 250m - a lot). You will also need the storage later, and having it before starting the gun upgrade will save you time, and make your upgrade more fluent. With a full storage of 9000e you need only 6000 energy that you need to make during the building time. This means that you need only about +150e/s income, to be able make gun upgrade. When you see that your enemy has T2 tanks, or your enemy has gun upgrade, the range upgrade allows you to kill T2 units with OC them from long range, and completely deny the enemy tech advantage. You have 5 more range than a non-Aeon gun ACU, so you can kite him - but you need to pay full attention to your ACU, or you could die, but with good micro you enemy would explode (if not from your ACU, then because of the frustration that he isn't able to hit your ACU) .
Another Great strategy is to abuse the T1 bomber: they have a very solid aoe (4) and 200dps. When you have secured air, (because you need it) it is the time to make some bombers, one pass wont kill units lke enemy bombers kill your Auroras, but it will damage them and make them very vulnerable, which gives you an advantage when the enemy thinks that he has plenty of units, but in really they don't have much hp and will easily die, so you can owerhelm his acu, and its an easy win for you.
During the T1 stage, Aeon is very strong, if microed correctly.
You have the best T2 air units - Swiftwinds, that secure you total air dominance. However your lack of fighter bombers mean you lack sniping capabilities against targets protect by flak. You have a very strong ACU, with range upgrades, and enough energy for Overcharge you can stay in the battlefield for much longer and vaporize enemy T2 forces from long range, and make your force feel safe and comfortable close your ACU.
About land, the best Aeon T2 unit is the mobile shield. however, its needs energy (-75/s), but it gives your force 3600hp - Auroras dont have hp and this removes their weakness. Also you have the strongest (but not the best) T2 units - the mighty Obsidian tank, whith has an incredible 2750hp and deals 480 damage per shot. However its a very expensive unit that is quite useless against the enemy ACU - they are slow and have low range that makes them vulnerable to Overcharge (you can easily kill 3 in one shot) so try to avoid using Obsidians against ACUs, or be sure that they don't have energy storage. But when you can spread your forces apart, and you wont meet the ACU, then Obsidians with mobile shields (3 obsi + 1 shield +1 T1 artillery/flak - if he has T2 air - in factory queue) are the best choice which starts to give your opponent questions like "how i can kill this shit?"
As a bonus, you have the kamikaze T2 air units - Mercy, that deal 2400 amage (but only once). But making Mercies is always a gamble, and very risky, if the enemy scouts and destroys them, you lose a lot of mass for nothing. When you want to use Mercies, then you need know where the enemy ACU is, and be sure that he doesn't have air, or AA around. It is possible distract the enemy inties, or force enemy mobile AA to fire for your first inties, and then attack with the Mercies, but its requires skill and practice. Also its a very risky move. When I decide its a good time to troll enemy a bit, I find enemy ACU, go with my ACU and army against him, and try to deal some damage, lose some of my force, let him think he has the advantage and retreat with words like "omg shit, you let me live!" stay with ACU at long range (its important) and then come with some Mercies; you don't need a lot, in most games is 1-2 enough to kill his ACU, and stay alive with about 4K hp on your own ACU. GG easy. When you do air, you can't spend as much mass on land, so you need think about it.
What is worth mentioning is Aeon have cheapest TML that costs only 700 mass instead of 800/850. During the T2 phase you need to use your ACU to Over Charge enemy units from range, and not let the enemy ACU Overcharge your Obsidians, while securing air dominance with Swiftwinds.
You also have T2 hover tanks with a high speed but they are not as effective as Pillars and cost more. Bear that in mind. And don't forget that the best Aeon T2 units are mobile shields.
Other T2 phase are better than Aeon. They have the Obsidians, but you can't really fight the ACU, so a valid strategy is to try to rush T3 land, and make harbingers.
Harbingers are fast, and very powerful early t3 units. They wreck T1 in one shot and if kited kill T2 unit groups and after they can reclaim them and send you mass from the dead souls of enemy units. But when the enemy has percivals/bricks on the field, then it starts to be difficult for Harbingers to stay effective. Its never a bad idea to make t2 mobile shields with Harbingers.