My advice may not be as great as what others can offer, but to give some general advice that might help:
Be sure to prioritize buildings such as libraries, universities, National College, Oxford University, etc. They'll contribute the most towards science per turn as any civ and are your backbone for keeping up in techs. Since you're playing on normal difficulty, you should be able to construct Great Library (one of the best wonders in the game, and great for science) without it being taken from you. When given the option to choose a free tech, such as when you complete Oxford or when a spy manages to steal one from an AI player, pick techs that would take the most turns to research.
While you're correct in that the Iroquois and Ottomans aren't exactly the strongest civs in the game (far from it), Babylon and Korea are often considered among the top 3 civs in the game alongside Poland, and those two are also known for maximizing science the best of any Civ. Babylon in particular gives you a free Great Scientist when discovering writing. Don't use the one-time effect of giving you a science boost, and instead use it to construct an academy, as early on in the game, it'll allow you to accumulate a large quantity of science over time. When to stop constructing academies and when to begin using the one-time effect is best left to your judgment. If you're behind on techs compared to other players after that, consider enacting Scholars in Residence at the World Congress, or by placing your spies in the cities of civilizations that have the most techs.
As far as Military goes, it should be noted that the AI is notoriously poor with using armies, and that should an enemy AI declare war on you, it's possible to stave them off with a fraction of their military might. When trying to conquer other civs, be sure to take diplomacy into account (being ganged up on by multiple civs is not ideal but it sometimes might be unavoidable). Additionally, take into account the composition of your army- mainly the ratio of melee/gunpowder/ranged/siege units compared to one another.
And lastly, general advice would be to know which wonders are worth constructing and which ones are worth best skipping. It's a common mistake (that I'm guilty of too) to go wonder hunting and as a result, neglect constructing basic buildings like libraries, markets, etc. The earlier you get these basic buildings, the better off you'll be.
Apologies if this was lengthy, but hopefully it covered a few points that might help you out!
The victory condition I set is military or scientific. I play on normal. I like the challenge these civs bring and do not want civs that guaranty that I will win, for example Poland, which I think is an expansion pack.
