May somebody use oddball paradigm solely for psychophysical studies?
First off, I'm not an expert, but the oddball paradigm was initially developed for use in event-related potential (ERP) studies (basically EEG measures) (source: Wikipedia). Hence, because of historical reasons, you see this paradigm pop up especially in ERP studies. However, the task has been used in purely psychophysical experiments as well, without EEG or imaging (e.g., Stockdale et al. (2011)). 

Reference
- Stockdale et al., Vis Res (2011); 51(11): 1232–8