if you think the mayans are weak you need to start building the pyramid sooner; they're basically a more flexible babylon with their unique ability too
the huns are actually more flexible than people give them credit for; free animal husbandry means a good bit of extra potential early production from horses and pastures and also frees them up to research other things in the early game, giving them a nice head start in far more than just military, which means a lot in a game like civ where early advantages easily snowball into monstrous leads
the celts are actually pretty decent; they're one of the few civs that are effectively guaranteed an early religion, and that means a tailor-made set of bonuses that can be incredibly strong depending on your surroundings and what victory you go for; the ceilidh hall is also a pretty good building, more happiness is always a good thing
brazil is possibly the best civ for cultural victory, the tourism bonus from carnival is just that huge. the jungle bias means they'll be suffering a bit early on from lack of production pretty often but it also makes them very hard to invade, so they have a sort of passive defensive bonus too; brazilwood camps are also really good
as for the other civs you were wondering about:
byzantium: potentially very strong if you can get an early religion, but they're the only religion-based civ that doesn't have any faith bonuses, so this is far from guaranteed; as for their units, the cataphract is pretty boring, but the dromon is quite good, it makes byzantium the only civ with ranged naval units before medieval
polynesia: very, very situational, the oceangoing ability is very map-dependent for how useful it'll be, but it does usually mean you'll establish the world congress first; the moai are nice, but having them means having tiles that aren't farms or mines, which in the long run will usually hurt you. maori warrior is ok
carthage: the ability to go over mountains is fairly weak; it does give you the ability to build roads over mountains, and gives you some tactical options no one else has, but ultimately doesn't come into play often enough to be very relevant; the free harbors are nice, but also aren't a very strong ability on their own; the main utility for them is the synergy with the Exploration policy tree and the Liberty tree, which makes founding new coastal cities cost no happiness penalties
ethiopia: stele is a strong candidate for best unique building in the game, guarantees you'll get the first or second religion 99% of the time; their other bonuses are nice but are nowhere near as impactful
india: not much to say here, not a very exciting civ; interesting thing to note is that the unique ability makes each city give less unhappiness than usual once it has 6 population or more, which counterintuitively makes india one of the best city spamming civs
morocco: this is a nice civ if you like gold; the bonus it gives means other civs will be more inclined to trade with you, which means they're less likely to attack you since you're giving them gold so it also doubles as a sort-of defensive bonus; the kasbah is useless on flat desert tiles though
netherlands: polders are really good, but really situational; the luxury ability gives you a lot of extra trading power; sea beggars are an improvement on an already decent unit
portugal: probably the best civ as far as gold income goes after venice, the feitoria is nice too if not particularly exciting; naus aren't anything special but more gold is more gold
siam: the bonuses from city-states is a lot stronger than you might think, and they actually make siam one of the strongest civs because they get so much more early food/culture/faith than other civs if they maintain relations with city-states, which you really should be trying to do anyway
holy shit i think this is the biggest post i have ever made