Does the duration of the epoch of interest in fMRI need to be a multiple of TR? I am designing an fMRI experiment whereby, for each trial, subjects need to listen to an auditory stimulus (of arbitrary duration), and subsequently give a rating for each stimulus. 

I intend to compare the BOLD signal for the different conditions under which that stimulus is presented. Thus, the part (epoch) of the trial that is of interest for analyses (contrasts) is when the stimulus is presented. 

My question: is there any reason (to do perhaps with MR physics or statistical analyses) whereby the duration of the epoch of interest (i.e. of the auditory stimuli) should be an integer multiple of the TR, or can this really be arbitrary?
The biology underlying the BOLD response is much slower than typical TRs, so I would say on one hand it doesn't really matter because the TR interval is not the time scale that matters. On the other hand, if you are presenting stimuli of duration where the TR matters, those stimuli are occurring too quickly to be resolved separately using fMRI. You may be able to solve this problem by averaging over many stimulus presentations with orders in different combinations, but that may increase your scan time more than having space between epochs and requires independence assumptions that are likely to be inappropriate.

In summary, look at the structure of some auditory fMRI tasks and see how they are organized before designing your own.