Overpowered:
Carthage
Not sure why this civ gets a "free pass" but it's the only civ I will sometimes re-roll due to just steam rolling everyone. This civ has so many things going for them. The biggest is the roadless trade network if you stick to costal cities. (As Carthage you mostly should) The Quinquereme insures that no one else will be making costal cities and is great for forcing heavy tribute. It's bonus to international trade routes though not a big deal on its own, works with the roadless network to help insure you always have a massive gold income. The instant gold on city building though has been reduced to less insane levels just adds more gold to an already gold heavy civ.
Indonesia
Though not overpowered to the degree of Carthage, it's an highly ignored civ. Indonesia has the crazy ability of multiple free unique resources. This means there are no "useless" city locations because you will always have resources to work. You're also guaranteed several monopolies. Their UU the Kriss Swordsman is also crazy good. VP has removed the negative effects, so only the super powerful ones remain. This allows you to attack your neighbors early and make sure they won't be a threat.
Zulu
The recent (and in my opinion, unneeded) changes make the Zulu stupid powerful. They are a total warfare civ, and they do it crazy good. I won't list everything because it's been discussed to death already, but being able to camp out in a defeated but not peaced out civ to farm experience is gamey and overpowered. The Impi are hands down the most powerful unit for their time. They gain the already crazy powers the Zulu have but get a "free" attack on top of it. Their only downside is you gain them somewhat late, though not that late.
Underpowered:
America
This poor forgeten civ.. has nothing really going for it. It's UA, though on paper seems pretty good, in practice quickly becomes "meh". Tile buy out doesn't give that much production compared to tile cost. Considering how tiles just keep costing more as you progress it's really only good to rush an early wonder. After that it becomes a small bonus that you get when you buy out tiles that you would have bought out anyways. Tile buy out also scales horribly with game speed, so on Epic and Marathon your production for gold spent quickly spirals into pointlessness. The +1 sight on combat units is "ok". Their UB is a slightly better version of the original, but because is a NW you can only build one. Tile stealing, again, though on paper seems powerful, in practice I hardly ever use it. They also lack victory focus like other civs do, they are a weak generalist civ. The AI is super horrible playing America and never creeps past a mid power level ranking. Their UU is good, but gained usually too late to make a massive impact.
Austria
I don't play them that often, but when I do I find them underwhelming. When everything happens to line up nice and you don't roll civs that can mess with your city states, they can do well.. but any civ can do well if everything lines up correctly.
Venice
Despite the slow attempt to change Venice from a true one city civ (changes I don't agree with), Venice in the hands of the AI never does well. Humans somewhat better, though the random number gods play a role in this. City state placement and resource placement can make or break Venice.
