How has Iran's global influence grown?
Power is the ability to make others do stuff they'd rather not.
...like run out of oil?
Closing the strait (note, it is not straight, it has a fairly sharp bend) is hugely influential, and by allowing certain vessels to pass, while prohibiting others, Iran has gained at least some degree of new influence over nations such as China and India (who between them constitute a quarter of the world), and are also able to bolster the Russian economy and strengthen that country's ties to Iran, which in turn allows Iran to rebuild her military.