I am currently playing immortal - large continents - domination game with Zulu and OH MY GOD.
These African guys are insanely powerful.
I managed to conquer my entire continent (5 civs) before the renaissance, out teched for most of the time, with only 3 - 4 decent "home" cities and with GPT below zero for most of the time (Honor finisher is absolutely awesome).
Many people see power of their low melee maintenance, but I fell in love with -25% experience required for promotions. That combined with Honor allowed me to have melee units with march + blitz or ranged units with range + logistics in the medieval age. Impi are a bit overrated because "pure" Impi aren't that good (additional weak attack is nice, but not incredible), they become terrifying because of all those Zulu UA bonuses and UB promotions.
Melee/gun units with 3 movement, +30% resistance to ranged attacks, bonus to flanking, +10% to power and +10% to power in the open terrain, plus insanely fast experience gaining (half of my army is healing every turn, able to attack two times and having ~50% bonus in any terrain), great generals and discipline =
I don't know if Zulu are OP, they are IMHO the best war civilization.
Mongolia has the best UU in game, which is almost invicidible when correctly used, but it stops shining in late renaissance (?), later and before you have only generals healing fast.
Huns are able to rush enemies extremely early, but their best times pass also really early, and you are left only with +1 from pastures.
Assyria can capture cities easy, and solves technological problem of warmongering, but they have no bonuses to, uhm, "pure combat".
Japan has decent UA, decent Samurai and absolutely useless Zero
Nothing spectacular.
Rome, Germany, Ottomans, England are good warmongers in certain circumstances. Denmark is uhm at least controversial
On the other hand, Zulu have very universal bonuses which make them always terrifying. In the very early game melee maintenance ability allows them to have bigger armies in poor times, in the early medieval/late classical age they can devastate the entire continent and all civilizations with Impi, and they enter into Renaissance with entire army experienced and absolutely elite infantry (with all those Bull promotions, post - Impi promotions and so on). IMHO they are overall the best in combat.
The only civ I would call OP would be eventually Babylon, with +8 to science at writing (scientist -> academy), this is really hard to beat. Still, I'm not sure if this is enough powerful to be called overpowered.