Guitar strings struck out of phase Do guitar strings struck out of phase with one another force each other to begin vibrating in phase with one another? I ask because wouldn’t chords sound more dissonant from time to time if this did not happen?
 A: Yes and no.  In the phenomenon you're referring to, called "entrainment", the relative phase of two weakly coupled oscillators whose fundamental frequencies are nearly the same will tend to become constant.  This does not mean their phases will be the same; only that the phase difference will be constant. 
Something very similar can happen between two oscillators when their fundamental frequencies are different but there is a close match between harmonics of the fundamental frequencies (not necessarily the same harmonics).  
You asked: 

Do guitar strings struck out of phase with one another force each other to begin vibrating in phase with one another? I ask because wouldn’t chords sound more dissonant from time to time if this did not happen?

When the harmonics of a fundamental note are played together on separate strings, it forms a chord.  So, the strings in a guitar chord have at least some harmonics that match up with each other.  It seems plausible, then, that strings very slightly out of tune could be fingered to form a chord and entrainment would cause them to vibrate together as if they were actually precisely in tune.
However, I doubt that this entrainment happens in practice unless the strings are very nearly in tune and there are no disturbing influences such as environmental acoustic noise. Any time you hear a guitar you can be sure there is plenty of acoustic noise to interfere with entrainment. And even if there were no acoustic noise, entrainment is a slow process.  So the answer to the first part of your question is "yes in principle, but not in practice".
In practice, when two pure tones are slightly different we hear a beat frequency corresponding to the frequency difference between the two tones.  This principle is often used in tuning a guitar: play an open string and a fingered string that produce the same note, and you will hear a beat frequency if they aren't exactly in tune.  You can hear the frequency difference.  In fact, what you hear will be closely related to the linearly changing phase difference between the two tones.  If the frequency difference between them is 1 Hz, their relative phase will shift linearly at the rate of 2 pi in one second.  If both tones have the same amplitude, they cancel out whenever their relative phase is an odd integer multiple of pi, and they reinforce whenever their relative phase is an even integer multiple of pi.  Together, they go through a quiet/loud cycle once per second.  If that quiet/loud cycle period is much less than a second it's annoying and we call it dissonance.  If it's much more than a second it comes across as vibrato which some people love. 
So the answer to the second part of your question is that if we don't hear dissonance when two strings are played together but are slightly out of tune with respect to each other, it is most likely our perception of the sound (not entrainment) that makes the sound seem non-dissonant.
