Do large-scale modes of variability (like NAM/SAM/ENSO) exist in the ocean? Large-scale patterns of climate variability can be explained at this Annular Modes Website.

If so, have they been characterized by EOF analysis in the same way that the annular modes in the atmosphere have been characterized? Where would be able to find this?
The large scale modes of variability present in the atmosphere are also found in the ocean. There is a strong feedback between the two systems with wind, heat flux and atmospheric pressure modifying ocean surface conditions and with parameters such as sea surface temperature altering atmospheric conditions. 

A lot of studies have explored teleconnections in the ocean looking for instance at the EOFs of sea surface temperature. A good compilation of different atmospheric and oceanic time series and references can be found in Climate Indices: Monthly Atmospheric and Ocean Time Series.