In a 4/4 instrumental for example: If I have to put stressed syllables on the strong beats of the instrumental, What happens to the other beats that might get stressed acedentally since it's unavoidable to write stressed syllables on weak beats? Does it make the song sound bad? Or do the stressed syllables on the strong beats(in this case, beats 1 and 3) just sound more accented than the ones on weak beats?
I think you've got this the wrong way round. The lyrics will have more emphasis on what the time signature is than the other way round. Lyrics usually make their own rhythm, thus dictating where they go in the bar - be it 4/4, 3/4 or whatever.
In 4/4, yes, convention says there is beat 1 that is strongest, beat 3 next, with 2 and 4 (and those '&' bits) next. That's basically the way we recognise and name time signatures.However, many, many pop type songs seem to have nothing - no emphasis - on beat 1. The word (or note) that belongs there is pushed forward, to be sung/played on the & of 4 of the preceding bar. So, no emphasis at all on beat 1, but we still feel it there.
So, what you're considering isn't particularly a consideration. You're putting the cart before the horse, as we say. Stop thinking about the 'problem' in the way you describe, and look at it from just about any other angle.
By simply saying the words you want to use in a rhythmic manner, you'll find the natural way they'll come over when put to music. Unless you want something more avant garde, of course. But most songs reflect that natural pattern - that's one of the main considerations that good songwriters keep in mind.
Mostly, songwriters work on making the rhythms of lyrics and the musical stress agree. When this principle is poorly applied, the lyrics may not be heard correctly. I assume it's worse in tonal languages.
A couple of examples I remember are "All we like sheep, have gone astray" which sounds like "Aw, we like sheep, aw, we like sheep, aw, we like sheep have gone astray. The other is Enrique Iglesias' "Bailamos" which gets the stress (agogic rather than emphasis) on "most" rather than on "Bai."
I think you need to remember that the beat accenting of meter is conceptual. You do not need to literally accent metrically strong beats to create/be in a particular meter. The obvious example of this is syncopation where a meter is established, and the conceptual strong beats are understood, but the actual rhythms shift accents off the metrically strong beats.
...If I have to put stressed syllables on the strong beats...
You do not need to do that. It isn't a requirement of writing music.
Just look at the song Ac-cent-tchu-ate the Positive. From a dictionary the syllable stresses for the word "accentuate" are weak on the first syllable "ac" and strong on the second syllable "cent." Yet in the song, the weakly accented first syllable is given a musically strong first beat accent!
Interesting to me is the fact that I completely misunderstood the lyrics of that song when I was a little kid. I though the lyrics were "you got the accent, oh ain't you positive?" The word "accent" does actually stress the first syllable and so that seems to explain why I misunderstood the lyric. Good prosody, bad prosody? It certainly is not a one to one match up of dictionary syllable stresses with musical meter stresses... but it was a darn successful song.
The insightful thing to recognize in that song is the actual prosody being employed. If a speaker wants to accentuate a word, one way to do it is strongly stress and evenly space all syllables. Like if someone were mumbling and another said "WOULD-YOU-PLEASE-E-NUN-CI-ATE?!" The song Ac-cent-tchu-ate the Positive is doing something similar. It's emphatically telling people to accentuate the positive and so it stresses nearly all the syllables of the word: "AC-CEN-tu-ATE". (The lower case "tu" is metrically unaccented.)
Prosody in the linguistic sense isn't just about dictionary accents. It's about how language is actually spoken. Prosody in the musical sense - setting text to music - will depend on how that text would be spoken naturally. And there are no absolute rules of correctness for either sense of prosody.
...What happens to the other beats that might get stressed acedentally since it's unavoidable to write stressed syllables on weak beats? Does it make the song sound bad?
If you put accents on weak beats, it is syncopation.
It isn't unavoidable to write stressed syllables on weak beats. Scansion is a concept to look up, it's about finding the rhythm of a line of text. Keep in mind that text patterns like
strong weak weak, etc. do not necessarily require particular meters.
Strong weak weak is a pattern of three "events" but that doesn't necessarily need to be a meter of three. It could be a pattern of steady eighth notes in 6/8, it could be a pattern of half note, quarter note, quarter note in 4/4, etc.
Rhythms that confirm meter versus contradict meter should not be equated to good versus bad. Both are valid. You should use the rhythms that express your idea. I don't want to over generalize, but it seems like some guideline would be helpful. Meter confirming rhythms sort of work within expectations and can convey feelings from gentle and relaxing to strong and confident. Syncopated rhythms work more on surprise and are exciting or agitated. Again, those are very broad and subjective generalizations, but they give some sense of how you might use rhythm. (Mode, tempo, dynamics, timbre will also effect mood and expression.) I would say the only bad thing it to use rhythm haphazardly.
From the comments, I get the sense that both you (the asker of the question) and we (those considering answering it) are struggling because the "rule" that calls for strong syllables to be on strong beats is not terribly strict, and, more significantly, because the identity of the "strong beat" is somewhat fluid thanks to syncopation and similar aspects of rhythmic and metrical complexity.
Take, for example, Twinkle, Twinkle, Little Star.
X:1 L:1/4 M:2/4 K:C V:1 clef=treble CC | GG | AA | G2 | FF | EE | DD | C2 | GG | FF | EE | D2 w:Twin-kle, twin-kle, lit-tle star; how I won-der what you are. Up a-bove the world so high...
Thanks to the magic of poetic meter, you can set any seven-syllable line to the same notes so long as it starts with a strong syllable and then alternates. An example is "Jack and Jill went up the hill."
X:1 L:1/4 M:2/4 K:C V:1 clef=treble CC|GG|AA|G2 w:Jack and Jill went up the hill...
But the next line of that poem does not fit the melody of Twinkle, Twinkle even though both have seven syllables. You end up with TO fetch A pail OF wa-TER.
X:1 L:1/4 M:2/4 K:C V:1 clef=treble CC|GG|AA|G2|FF|EE|DD|C2 w:Jack and Jill went up the hill, to fetch a pail of wa-ter.
That's clearly wrong. But look at the opening line of Gangsta's Paradise:
X:1 L:1/8 M:4/4 K:Cm clef=treble style=x EE|F2 FF GG GG | AA A(A A)A =BB| w:As I walk through the val-ley of the sha-dow of death,_ I take a =BB B(B B)B BB|c2 cc c(c c2)| w:look at my life_ and re-a-lize there's no-thing left.
Or of Sondheim's Marry Me a Little:
X:1 L:1/8 M:4/4 K:B V:1 clef=treble z2zFE2(F2|F3)D EAz2|z2zGF2(G2|G3)FB,2z2| w:Mar-ry me_ a lit-tle, Love me just_ e-nough.
Are these wrong? No, they are genius. Why?
One reason is that the strong beat is shifted. In Gangsta's Paradise, it's a classic anticipation of the strong beat that can also be heard, for example, in Joplin's Maple Leaf Rag. In Marry Me, Sondheim is actually using a complex meter with six beats of unequal lengths spread over two measures, so it could have been notated as (3+3+3+3+2+2)/8. The strong syllables actually do coincide with the strong beats if you analyze it that way.
But with Gangsta's Paradise, there's something else going on. The second syllable of realize is stressed even though it isn't normally. This would be wrong in a Sondheim song (I'm basing that on my having seen a few interviews in which Sondheim discusses songwriting, often with a good degree of self criticism), but here it is more of a musical and rhetorical device, creating rhythmic interest and calling the listener's attention to "realize," a word which is central to the meaning of the poem.