May I suggest that you put some strings on a simple 1/2" thick piece of wood, put a mic near the strings, and see if that's a sound you really want?
The strings themselves make hardly any noise: they are thin and slip easily through the air without making much of disturbance - and a sound wave is a disturbance of the air. An
acoustic guitar would be much quieter without the vibrations of its bridge and body. In an acoustic guitar, the vibration of the string is transferred via the bridge and saddle to the top plate body of the guitar.
The body
The body serves to transmit the vibration of the bridge into vibration of the air around it. For this it needs a relatively large surface area so that it can push a reasonable amount of air backwards and forwards. The top plate is made so that it can vibrate up and down relatively easily. It is usually made of spruce or another light, springy wood, about 2.5 mm thick.
On the inside of the plate is a series of braces. These strengthen the plate. An important function is to keep the plate flat, despite the action of the strings which tends to make the saddle rotate. The braces also affect the way in which the top plate vibrates. The back plate is much less important acoustically for most frequencies, partly because it is held against the player's body. The sides of the guitar do not vibrate much in the direction perpendicular to their surface, and so do not radiate much sound.
The air inside
The air inside the body is quite important, especially for the low range on the instrument. It can vibrate a little like the air in a bottle when you blow across the top. In fact if you sing a note somewhere between F#2 and A2 (it depends on the guitar) while holding your ear close to the sound hole, you will hear the air in the body resonating. This is called the Helmholtz resonance and is introduced below.
Another way to hear the effect of this resonance is to play the open A string and, while it is sounding, move a piece of cardboard or paper back and forth across the sound hole. This stops the resonance (or shifts it to a lower frequency) and you will notice the loss of bass response when you close up the hole. The air inside is also coupled effectively to the lowest resonance of the top plate. Together they give a strong resonance at about an octave above the main air resonance. The air also couples the motion of the top and back plates to some extent.
The Helmholtz resonance of a guitar is due to the air at the soundhole oscillating, driven by the springiness of the air inside the body. I expect that everyone has blown across the top of a bottle and enjoyed the surprisingly low pitched note that results. This lowest guitar resonance is similar. Air is springy: when you compress it, its pressure increases.
Consider a 'lump' of air at the sound hole. If this moves into the body a small distance, it compresses the internal air. That pressure now drives the 'lump' of air out but, when it gets to its original position, its momentum takes it on outside the body a small distance. This rarifies the air inside the body, which then sucks the 'lump' of air back in. It can thus vibrate like a mass on a spring. In practice, it is not just the compression of the air in the body, but also the distension of the body itself which generates the higher pressure.
To complicate things even further, the guitar top moves differently, depending on the note played. To see how the guitar top moves at different notes, there are visual tests called "Chladni Patterns". Here's an example:
http://www.phys.unsw.edu.au/~jw/guitar/patterns_engl.html
Finally, your statement of "It seems that the Shure SM57/58 mics use the same capsule. Just different mic body. So I'm guessing that a lot of the cardioid mics are the same capsule as the omni mics of the same brand/series." is wrong. No vents in an omni, but vents are needed in a cardioid mic. AFAIK, there is no Shure Omni mic that uses an SM57/58 capsule.