Yes, those verses do bother me. And you're right, one's answer to this will cut to the point of their view of Scripture and its inspiration. So, at the risk of joining you in the boiling pot, let me offer my opinion and its rational support.
I reject absolutely the idea that the Bible is inerrant in every way. There are quite clearly historical and/or scientific errors in its record. Even apart from this, we must ask about the human writers through whom God worked. It seems the only way for God to ensure that absolutely every word was precisely what He wanted would be for Him to forcibly move the quill as He desired. Thus, we can admit of human error; or, to be more precise, human bias. We see cursing Psalms expressing decidedly un-loving attitudes (39, 69, 109); we see God making bargains with the devil (the Book of Job); we even see Jesus Himself expressing historical ignorance (Matt. 16:28, Mark 9:1, Luke 9:27). I reject utterly the idea that the Bible is absolutely consistent and completely without error; I also reject utterly the idea that this makes it worthless or of low worth.
We can easily see Paul's biases, at least on a superficial glance: he wears them on his sleeve. He apparently believes that marriage is merely a substitute for lust; he apparently believes that women should cover their heads and shut up in church; and he apparently believes that women are to blame for this whole sin mess and that they are cleansed by the pain of childbirth. It is interesting: in any piece of literature except Scripture, we would analyze him and say that he probably had some serious issues with women, most likely stemming from an unresolved Oedipal complex or some abuse in childhood. I think we ought not ignore these passages as uncomfortable; no Scripture should be given that treatment. Instead, we should explore what that meant to the original writer and the original audience, and see what we can draw from it.
As I have already said, it is clear where Paul's biases seem to lie. No other Biblical author speaks out so frequently or so radically against women's actions. But let us see what else Paul says about women:
1) He makes no distinctions between men and women in light of Christ (Gal. 3:28)
2) He speaks approvingly of women praying and proclaiming God's message in public worship (1 Cor. 11:5)
3) He refers to several women whom he instituted and/or approved for leadership over a church (Rom. 16)
4) He admonishes husbands to love their wives in a sacrificial way, which was unheard of in that time period (Eph. 5:25, 28; Col. 3:19)
Partially in light of these inconsistencies, and partially due to extant manuscripts, many scholars believe that the 1 Cor. 14 admonition is a later addition, especially in light of Paul's praise of women speaking out in church merely three chapters earlier. Thus, there is some doubt that this is actually Paul talking and not some later mysogynistic scribe. If it is Paul, however, while it seems that this is a clear case of his bias against women, is it necessary that we view it that way?
Let's look now at the intended audience. Paul is writing a letter to the Corinthians, a notoriously rowdy and randy bunch who frequently bent the rules of good conduct to suit their patterns of behavior. More than once, Paul had to lay down the law with them. Paul speaks in his other writings of "spiritual milk" and "solid food", and how certain Christians are deserving of each. He also speaks about not causing a brother to stumble, and abstaining from practices which are acceptable in God's eyes because indulging in them might lead a weaker brother to sin. Is it so unreasonable, given the intended audience, that Paul is giving spiritual milk teachings to weak Christians, not claiming that the thing is in and of itself bad, but that it is best to avoid it altogether to avoid any appearance of impropriety and to keep others strong in their walk? It is entirely possible that (assuming the passage is truly Pauline) he got a little carried away in his rhetoric, given his frustration with this church.
Either Paul allowed women to speak in church, or he didn't. 1 Cor. 11:2 indicates that he did; 1 Cor. 14:33 indicates he didn't. Which are we to believe is the better universal mandate? The former has a much better argument for it, since it has reason, justice, and spiritual solid food on its side.