We know he was a Sith, but was he actually a member of the evil Empire? From what I have researched I can not find his rank. He seemed to be more of just an acquaintance of Palpatine. But then why does the imperial army respect him as if he were a Commander, able to give orders, and commandeer a TIE fighter? Even Grand Moff Tarkin (dis)respected him.
According to Wookiepedia, Vader did hold an official Imperial post: Supreme Commander of the Imperial forces.
However, as you note, he was for a time subordinate to Grand Moff Tarkin. From Wookiepedia:
During the Battle of Yavin, Lord Vader was apparently only Palpatine's observer aboard the Death Star, with operational control in the hands of Grand Moff Wilhuff Tarkin, who was clearly capable of "holding Vader's leash"; soon after, however, he was given command of the forces charged with prosecuting the war against the Rebel Alliance, and perhaps a wider commission to maintain order throughout Imperial space. His new powers may be presumed to have been conferred by the time he returned to destroy the Rebel base: by this point he had taken charge of Executor, the largest warship in the galaxy, as his command ship; and Admiral Griff and the Sector Group of the Bright Jewel Oversector—one of the most important Navy commands in the Empire—were subordinated to his command.
(I bolded key sections)
When the original Star Wars movie was scripted, Vader's position in the Imperial military hierarchy was indeed somewhat murky. Grand Moff Tarkin treated him as roughly equal, maybe even subordinate, and even many of the uniformed officers spoke to him as if he weren't as important as he really was (that high officer who gets Force-choked, for instance, would have been killed outright had he done the same in ESB).
By ESB, "Lord Vader" was firmly established as Commander-In-Chief of pretty much every Imperial within comms range. This seems, in the context of G-canon and of the EU, to have been an assignment made by Palpatine after the Battle of Yavin. By the end of Ep III, Palpatine was the Supreme Commander of his fledgling Empire, and Vader simply his trained dog. After the Battle of Yavin, Palpatine handed over everyday high-level control of the military to Vader, both to have more direct control through Vader of the fleet to hopefully avoid repeating such a catastrophic loss, and so he could concentrate on this young upstart Skywalker. Of course, it's not much of a change; anything the Emperor wants done regarding the fleet, all he has to do is say it and Vader will do it.