I want to correct some misinformation contained in the top voted answer. The claim that this is a result of Handel poorly understanding English is pure nonsense; with regard to the (valid) complaint about the placement of stress in "For unto us a child is born," the music was almost directly lifted from an earlier duet of Handel: "Nò, di voi non vo' fidarmi." The initial stress makes PERFECT sense for this Italian text ("NO...I do not want to trust you, blind love, cruel beauty...") Take a listen here:
(I actually was somewhat shocked when I heard this for the first time and realized just how little Handel changed - though he added the defining homophonic chords on "Wonderful Counselor, Almighty God...etc.")
Oh, and if you stick around for the ending Allegro portion...it's "All we like sheep"! Again, almost directly lifted from the duet. It should say something that these two choruses are the ones that draw attention for their inappropriateness. It seems when Handel makes a stronger effort, things turn out quite well (remember that he composed this in about four weeks...will we begrudge him this?)
I think this should settle the question of why the text/music match here seems strange. However, the question of whether "All we like sheep" ought to be set to a more somber tune is a valid one. In the first place, it seems like Baroque (and early Classical) composers did not follow the "playful = fast and major, serious = slow and minor" rule quite as extensively as perhaps we assume they did. I know that Robert Levin makes this argument in justification of portions of his completion of Mozart's Great Mass in C minor, where critics make a similar "this text is too serious to be set to music like this" claim.
In the second place, I think everything else about Messiah should dissuade you from the opinion that Handel is just "trying to make a joke." I think that this choice was very intentional. The apparent disparity between the lively music and the dire text only serves to emphasize that "all we like sheep have gone astray," and "every one [has turned] to his own way." It stresses not only that sinners are flippant about God's law, but we are flippant about being flippant (i.e. we know we sin but still enjoy/do it). The aimless melismas and the opposite directions on "have gone astra-a-a-a-a-y" certainly emphasize the text in another fine example of Handel's word painting.
In short, you can't really claim in one place that Handel exemplifies good word painting ("Ev'ry valley" is the go-to example) and then turn around and say that these two choruses are poorly set because Handel "had a bad grasp of English." I don't think Handel was a native Italian speaker either and "Nò, di voi non vo' fidarmi" has that initial stress for all the right reasons. Sorry to make this so long, but the facts of this matter would be easily discovered by someone who took 5 minutes to read about these two choruses instead of just supplying their opinion.