Hmm...
The strengths of the Dutch, reasonably good if you like to play higher levels or micromanage trade. The polder is a lovely improvement that provides alot of food, and upgraded sea beggars are nasty. Weaknesses include the fact the UA is limited and you have to Live with .marshes till guilds. Maya is a science powerhouse, with its shrine replacement giving beakers, however the UU is a bit weak with few redeeming features. The UA gives free great people However you can only pick one once, and as time goes on it the gaps between great people widen. Furthermore each great person gained this way increases the cost of future great people. Cathages free harbours are a wonderful way to earn money fast, as well as gain extra hammers, however you should neglect building roads all together at your own peril if your on a contested landmass. UUs are good, and while mountain crossing can win.you wars,.in most games its useless. Will get to the others later, its not easy typing this on a phone
Now I'm back at my computer, i might do this properly
Austria - Haven't played them much outside of "Into the Renaissance" so cannot give a very accurate picture of them. But their UA is clearly one of the most powerful in the game, and probably deserving of a re-balance, perhaps increasing costs exponentially to marry into a citystate?
Byzantium - Its UA means its flexable, it can adapt to whatever conditions the map throws at you. The downside is of course, you have to found a religion, and your other uniques don't help much in that regard. I personally think the Dromon is an A class UU, it is ranged and can easily support your land units and dominate the water, park one in a city, to get an extra bombardment a full three eras before you get the Gallesess. Even Mighty Carthage will be shaking against a fleet of Dromons. Held off a hunnic invasion by simply using Dromons a few games back. the C - units, lets call them Armoured Ponies since I cant spell it, hold the interesting ability unique to other mounted units of getting terrain bonuses. As well as this they have higher attack. Alas the terrain bonuses and the bonus v naval dont upgrade. Basically the problem most people find with Byzantium is that the UU's doesn't match the UA very well
Carthage - Their UA is dual barreled. The Harbour part eliminates the need for roads, saving you a significant investment in gold, and allowing your cities to be connected up at the advent of the wheel. However the cost in this is you dont get the other benefit of roads, the movement cost reduction. This could make fighting and resupplying a war with a long supply line very difficult. Yet the gold increases are significant and powerful. Also you get increased hammers from sea resources, and seeing as Carthage starts on the sea, this will usually come into play. Mountian Crossing is a bit hit and miss, and will not likely come into play in a majority of maps. But if you can use it, it can often be a game changer. Protip, you can build roads over mountians if your willing to sacrifice the workers. The Elephant has a nice amount of bonuses and is a very useful horseman replacement, however its Terror promotion doesnt transfer over. The Quegmarine is a great unit for controlling the seas, but will need support or numbers if it wishes to take cities.
Celts - Havent played them much, so cant comment.
Dutch - Their UA is for advanced players and micromanagers, and for higher difficulty levels where the AI has more gold. If you do not actively play the trading game then you will find their UA nowhere near as good. Also, the benefits are rather focused to the start, being less useful in the later game. The UU upgrades into a monster destroyer. The Polder is a great improvement, however the downside is you wont always get Marsh starts as the Dutch, and you have to leave the marshes unimproved till Guilds, which can be annoying. The Sea Begger upgrades to absolutly awesome destroyers, and are powerful when propperly supported by Frigates
Ethiopia - I think this is the only civ that really punishes you for expanding, well that and India. The UA encorages you to go tall. And so if your a conquorer its best to pick another civ. Though I did have a good conquest game as Ethiopia, I ended up raising tons of cities, though. The UB is, in my mind, the best UB of the expansion. It guarantees you a religion, and at that, unless your playing at deity, first or second pick. Just War is a good religious pick, because it really complements your UA. The UU is an interesting one. Be warned though, while it may be strong around your capital, I've read posts stating that it actually looses strength below when a very far distant from the capital. Though I have not experianced this myself
Huns - Despite being a militarily focused Civ, their UA is focused not on millitary but on production. You can use this production to, of course produce millitary units, or you could use it to produce wonders. The UU's make you want to use your extra hammers for assault though, with the Battering Ram being exceptionally powerful in taking early cities, and the Horse Archer being useful to pepper the enemy cities. However despite this, it lacks a bronze age melee unit, having to use warriors till Civil Service or Ironworking, which for some might be a downfall. The UU's are also very early, and this will limit conquest a little.
Maya - On the outset, the UA seems very powerful, but what the description does not say is that you can only really pick one great person once (i.e, one scientist, one general), and that each one you do pick makes others more expensive. Some may consider this a downside, but really, I don't. The UU, I find, is not really that special. Sure its cheaper, sure it comes a tech earlier, but Archery isn't that expensive. it has no other redeeming qualities. The UB however is another story; and is the only UB to grant you extra science, it can be a real boost in the early game, because most people aiming for a religion make the shrine their second build. This makes the maya a strong science civ, in contention with Korea and Babylon.
I think I've got them all, I might have missed one. But that is the strengths and weaknesses of each of the new civs.