As far as I know the Ashikaga fell in 1573, but Tokugawa Ieyasu didn't take power until 1600, Toyotomi Hideyoshi had power but wasn't the Shogun. So who was?
There probably wasn't one. The country still was in the midst of civil war
There was fighting, with certain areas being controlled by certain warlords, but with no warlord leading the whole of Japan. Oda Nobunaga was on the brink of successfully uniting all of the warring states, but he was assassinated in 1582, after which time Toyotomi Hideyoshi became the front runner as the general under which the different states would unite. He was on top until his death in 1598, at which point Tokugawa Ieyasu stepped in and finally united the country for good.
Officially, the last Ashikaga Shogun (Yoshiaki) resigned in 1588. He was driven out of Kyoto and became a monk in 1573, but he still retained the title. Tokugawa Ieyasu took control of power in 1600 (mostly), but was not Shogun until 1603. From 1588 till 1603, no one officially held the title of Shogun. And from 1573 to 1603 there was no Shogun "ruling" Japan.