Analyzing the factors that determine our choice of visual search strategy could shed light on visual behavior in everyday situations. Previous results suggest that increasing task difficulty leads to more systematic search paths. Here we analyze observers' eye movements in an 'easy' conjunction search task and a 'difficult' shape search task to study visual search strategies in stereoscopic search displays with virtual depth induced by binocular disparity. Standard eye-movement variables -- such as fixation duration and initial saccade latency -- as well as new measures proposed here -- such as saccadic step size, relative saccadic selectivity, and x-y target distance -- revealed systematic effects on search dynamics in the horizontal-vertical plane throughout the search process. We found that in the 'easy' task, observers start with the processing of display items in the display center immediately after stimulus onset and subsequently move their gaze outwards, guided by extrafoveally perceived stimulus color. In contrast, the 'difficult' task induced an initial gaze shift to the upper-left display corner, followed by a systematic left-right and top-down search process. The only consistent depth effect was a trend of initial saccades in the easy task with smallest displays to the items closest to the observer. The results demonstrate the utility of eye-movement analysis for understanding search strategies and provide a first step toward studying search strategies in actual 3D scenarios.