After reading about the theme system and its development I have a feeling, that strategoi basically resembled feudal lords, having both civil and military authority over their themes.
To oversimplify things a bit, the Themata were the successors to the old military districts. After Rome was reduced to only Thrace and Anatolia, it became impractical to maintain the old separation between provincial and military administration. The hitherto professional Roman army was replaced with a system of small landowners who bred and raised their own horses and fought to protect their own estates.
The local farmer soldiers became the backbone of the Byzantine army, and as such the thematic borders tended to crystallize around where they settled (usually determined by the old Roman military district from whence they were derived). In comparison with systems from the old Roman west, the Byzantines gained the advantage of centralization at the expense of stability. The themes were generally not hereditary (but as the land owning families expanded, thematic positions in non-border themes could result in Grants going to the same family). The strategos would usually be appointed by Constantinople.