What is the standard way to analyze EEG data in a mismatch negativity paradigm?
Programs/packages for EEG analysis
There are decent MatLab toolboxes with good tutorials for for the analysis of EEG data. The EEGLAB toolbox (tutorial) can be operated by both GUI and command-line (and script). The fieldtrip toolbox (tutorial) is mainly operated by command line / script. 

Of course there are also (commercial) software packages for EEG analysis that do not require Matlab (e.g., BESA, Brain Vision Analyser, eeprobe), but I am not familiar with them. 

Are there techniques to avoid averaging out small ERPs whose latencies might vary?
No, probably not. ERPs are calculated by averaging across multiple trials because this averaging cancels out all components that jitter in time (that is, mostly noise), i.e. the thing you want to avoid (canceling out of jittering components) is actually the purpose of calculating ERPs.

However, to be sure you should have a look at reviews or tutorials for the measurement of the mismatch negativity. See for instance

Duncan CC, Barry RJ, Connolly JF, Fischer C, Michie PT, Näätänen R, Polich J, Reinvang I, Van Petten C. (2009) Event-related potentials in clinical research: guidelines for eliciting, recording, and quantifying mismatch negativity, P300, and N400. Clin Neurophysiol. 120(11):1883-908.  (pubmed)