Shiva is the Lord of Tapas. The power is the power of Tapas.

There is no particular connection between Shiva and the overmind -- the overmind is the higher station of all the Gods. It is better not to call it the overmind until the action of it is clear and there can be no mistake.
Mahashiva means a greater manifestation than that ordinarily worshipped as Shiva the creative dance of a greater Divine manifesting Power.

Brahma, Vishnu, Shiva are only three Powers and Personalities of the One Cosmic Godhead.

Of course, the gods exist, that is to say, there are Powers that stand above the world and transmit the divine workings. It is the physical mind which believes only what is physical and denies them. There are also beings of other worlds gods and Asuras, etc. There are gods everywhere on all the planes.

Power means strength and force, Shakti, which enables one to face all that can happen and to stand and overcome, also to carry out what the Divine will proposes. It can include many things, power over men, events, circumstances, means etc. But all this not of the mental or vital kind, but by an action through unity of consciousness with the Divine and with all things and beings.