Mayans
Pyramid (Faith + Science) equlas ICS monster
Atlatlist spam for early defense while REXing like crazy covering the continent with pyramids. Mayans can get a religion even on Diety every time and then enhance it with liberty's GP or the GP from The Long Count giving them a solid foundation for mid-late game conquest.
7 GP 4 free from UA + a guaranteed prophet + free one from liberty, all quite early. Who can match that?
Strategically placing cities not to expose to wide a front you can concentrate a stupid amount of units from your 12+ cities
How is this good for conquest? Well, churning out twice as many units as any opponent on diety while at the same time teching hard and having so much faith that you can by units or religious building avery 4 turns is indeed good for conquest. With pagodas lux problems from captured cities are mitigated, with holy warriors you can buy a crap ton of soldiers and later you can buy GE for juicy wonders or manufactories.
Chinese
More GG equals offensive citadels.
Better GG equals overcoming the disadvantage of being offensive,
Double attack Chu-Ko-Nu's that become gatling guns and machine guns means china is powerful from start to finish unlike some other civs that have to hit thier specific window of oppertunity. Also, you can skip logistics and get early range and march instead meaning you can actually "fully" upgrade these units without honour's extra XP.
Paper makes is meh but it will pay for itself and 2 units.
English
Extreme mobility on land and sea. Longbows are just stupid. You can conquer any other civ in medieval with them unless the terrain is extremely disadvantageous (all open terrain) and the enemy has a lot of mounted units.
Ship of the Line rules the sea for a very long time. With englands extra movement they will always get first strike and if they dont they can fire and escape.
Extra spy is always good. Instigate revolts in a militaristic CS behind enemy lines, steal extra tech or just keep track of backstabbers.
Aztecs
All offensive infantry you'll ever need will heal with each kill, move fast and get extra protection as long as you get enough Jaguars early on. Which you'll want anyway for scouting and extra culture.
Floating gardens are on the path to CB's and Swords.
Very tall, well defended(next to lakes with no ships in them) empire can focus their production meaning more blood-drinking units.
Go for left side of honor and continue with building jaguares and pissing off every AI near you by building an enormous city in their face to get a ton of culture and easy XP. Then kill everyone in the world and sacrifice them to the Great Serpent Ixiquatl...
Greece
I hate greece. Alex is in my opinion the most agreesive AI of them all and will DOW you on turn ~20 on diety with units as strong as something you will not have for another 50 turns... That's why YOU should play him
Sersiously 13 Stength spearmen and 14 strength horsemen that you can have after 5 techs on the path to chariot archers and CB's. the ponies also generate more generals which isn't to bad.
Concentrate on building units instead of food/happiness/culture because you can get that from a city state... Sell your lux to a neighbour and use the money to get it back from a CS along with some strategics and for a longer time. Or you could focus on building and allying some militaristic CS to get you some unique units that can change the war in your favour... Pretty cool. In fact, Hellas will reign supreme in my next game!