If it is ok, I also took the liberty of movig some info about his experiemtns with the Chitauri Scepter, from the "Captain America post credit scene" section to the section above, which contain the comic info, as I found it more fitting for it to be there. The comic described his experiments in greater detail.
When he recruited Smith, Strucker told him that he was from "annother part of the organisation, that seeks to provide a greater future for all mankind". Not a direct confirmation, but I interpreted it as he was a HYDRA-infiltrator inside SHIELD before the events of CATWS. If he officially was part of SHIELD, his "official" position was unspecified.