It seems there are so many cases in the Torah and Judaism that infer that women are 2nd class citizens, and have less rights than men. On the one hand the Torah and orthodox Judaism is eternal, but there must be a way to "right these wrongs", in modern society which, since feminism, sees women differently than when the Torah and Talmud were given thousands of years ago, and talk about Sotah, revoking vows and selling daughters!

Your question relates to a much broader topic, and that is, how in the world did Hashem manage to write and give a Torah 3,300 years ago, that will still be relevant forever, even in the most modern of times? A pretty "tough assignment", for if it was written in modern terms and wording [e.g. including computers, cars, surrogate mothers, prohibiting slaves, seeing women as today's world views them, etc.] our primitive idolatrous fore-fathers who had just been redeemed from slavery, would have "chucked" the whole Torah as something crazy and irrelevant. On the other hand, one of the primary goals of the Torah is precisely this, to help mankind mature both morally and spiritually, so it had to be relevant at the time of its giving, but simultaneously "eyeing" the eternal ideals to which it wants to educate and elevate us. Today, your very question is based on 3,300 (!) years of the Torah's advancing mankind, not too quickly but also not allowing man to stay where he was. Rav Kook brings the example, that the Torah would have preferred prohibiting eating meat, but mankind would not, and could not have said "Na'aseh v'Nishma" (="We will do and listen") to something so irrelevant, before soy proteins, substitutes, and modern vitamins, medicine and mindset, were around. So the Torah takes the pragmatic road, and taught man that even animals have feelings (all the mitzvot of "tza'ar ba'alei chaim"), 3,200 (!) years ahead of the ASPCA, but that being said, in the meanwhile, until we're ready, we are allowed to continue eating meat, but only when slaughtered in the most painless way, and not slaughtering the mother and son on the same day, etc. etc. We even don't bless "shehechiyanu" on leather, for we would have preferred not having to kill that animal. Thus, the Torah indirectly educated us "between the lines", that it's not really moral to eat meat. That in Gan Eden, in the ideal world, we were vegetarians; that Noach was only begrudgingly allowed to eat meat; that the only hunters in the Torah: Nimrod and Esav, are clearly negative personalities; meat for eating is called "lust meat" (basar hata'ava"), etc. etc. Yes, Lincoln freed the slaves, but this was a result (!) of the fact that the Torah, 3,200 years ahead of its time, already obligated us to treat slaves with respect and dignity, even when the world treated them as animals. Similarly, in a world that treated women almost as animals or slaves, came the Torah and taught us that women also have tzelem elokim (=the Godly spark God), are obligated like men in most mitzvot, and are the founders of Israel (no other ancient culture refers to matriarchs like patriarchs). But in order to be relevant, it had to address the world where it was at, a society where it took a week to do laundry, took hours to gather fire wood and make a meal, where obviously women didn't have careers, and weren't even educated. In other words, the Torah is meant for eternity, which means it had to be relevant 3,300 years ago addressing the lifestyle and the way women were seen then, but also relevant 3300 years from now, as well! So that explains the past, but what about today, when it seems like on some issues, modern society, albeit precisely because of 3300 years of Torah, may have even surpassed (!) the Torah on some moral issues? The answer is, the Torah, in order to be relevant in all times, just obligated the minimum (!), but every society is not only allowed, but even meant to add on additional moral obligations, whatever society is ready to digest. How is this done? The answer is simply: the Sanhedrin (the High Rabbinic Court which was in Jerusalem). All agree that "Tradition" is super-important to Judaism and we are correctly wary of reforms. On the other hand, all also agree with the importance of the rabbis of each generation to keep Judaism eternally relevant in a constantly changing world. The proper and original apparatus exactly geared for the harmony of these two ideals, is the Sanhedrin, which we have yet to revive. There is an obligation to do so and we must redouble our efforts to implement this mitzva, which also happens to historially be the very next stage in the redemption process [see Megilla 17b, following the revival of the Land of Israel, and gathering the exiles, as established, for that reason, in the order of the brachot of the Shmoneh Esreh, is "Hashiva Shoftenu k'varishona"]. We live in a unique period, which never was, and never will be again, in Jewish history. We have one foot already in redemption, while the other foot is still in "exile". We have the challenges and questions of redemption [unprecedented myriads of modern halachic questions, resulting from: miraculous and eschatological strides in technology, sociology and the modern State of Israel; as well as the gathering of the exiles, with their various customs and respective halachic traditions; not to mention what to do with 200,000 olim who aren't halachically Jewish; the changing role of women, etc…]; but don't yet have the framework, the Sanhedrin, to answer them. You heard me correct, I count your question regarding women's rights, as a positive issue, whose time for change has arrived. Until the Sanhedrin, local halachic authorities, continue to work alone, as they did for 2,000 years, and don't have the halachic "clout", nor the collective responsibility and authority, to make the necessary and far-reaching "updates". It is up to us to revive the Sanhedrin speedily in our day [it's actually easier than the previous 2 stages of geula which have already succeeded!], and return to normative and well-balanced Judaism. In the meantime, the God of History (who's obviously the same God Who gave us the Torah) has solved your specific questions, and decided long ago, that the issues of Sotah, vows and selling daughters, no longer apply, already for many centuries. So practically those and many other problems have already been solved, but it will be the Sanhedrin that will update certain other issues which demand change, like husbands who don't give gittin, etc.